Classical and Quantum Gravity - IOPscience

Classical and Quantum Gravity - IOPscience
Classical and Quantum Gravity
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Classical and Quantum Gravity
is an established journal for physicists, mathematicians and cosmologists in the fields of gravitation and the theory of spacetime. The journal is now the acknowledged world leader in classical relativity and all areas of quantum gravity.
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Open access
Gravitational lensing by spinning black holes in astrophysics, and in the movie
Interstellar
Oliver James
et al
2015
Class. Quantum Grav.
32
065001
View article
, Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar
PDF
, Gravitational lensing by spinning black holes in astrophysics, and in the movie Interstellar
Interstellar
is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this, our team at
Double Negative Visual Effects
, in collaboration with physicist Kip Thorne, developed a code called Double Negative Gravitational Renderer (DNGR) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering; and they differ from physicists’ image-generation techniques (which generally rely on individual light rays rather than ray bundles), and also differ from techniques previously used in the film industry’s CGI community. This paper has four purposes: (i) to describe DNGR for physicists and CGI practitioners, who may find interesting and useful some of our unconventional techniques. (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies; we focus on the shapes, sizes and influence of caustics and critical curves, the creation and annihilation of stellar images, the pattern of multiple images, and the influence of almost-trapped light rays, and we find similar results to the more familiar case of a camera far from the hole. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie
Interstellar
, were generated with DNGR—including, especially, the influences of (a) colour changes due to doppler and gravitational frequency shifts, (b) intensity changes due to the frequency shifts, (c) simulated camera lens flare, and (d) decisions that the film makers made about these influences and about the Gargantua’s spin, with the goal of producing images understandable for a mass audience. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of
Interstellar
interesting.
The following article is
Open access
Reversible dynamics with closed time-like curves and freedom of choice
Germain Tobar and Fabio Costa 2020
Class. Quantum Grav.
37
205011
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, Reversible dynamics with closed time-like curves and freedom of choice
PDF
, Reversible dynamics with closed time-like curves and freedom of choice
The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics compatible with non-trivial time travel, where observers in distinct regions of spacetime can perform arbitrary local operations with no contradiction arising. However, only scenarios with up to three regions have been fully characterised, revealing only one type of process where the observers can verify to both be in the past and future of each other. Here we extend this characterisation to an arbitrary number of regions and find that there exist several inequivalent processes that can only arise due to non-trivial time travel. This supports the view that complex dynamics is possible in the presence of CTCs, compatible with free choice of local operations and free of inconsistencies.
The following article is
Open access
A new understanding of Einstein–Rosen bridges
Enrique Gaztañaga
et al
2026
Class. Quantum Grav.
43
015023
View article
, A new understanding of Einstein–Rosen bridges
PDF
, A new understanding of Einstein–Rosen bridges
The formulation of quantum field theory in Minkowski spacetime, which emerges from the unification of special relativity and quantum mechanics, is based on treating time as a parameter, assuming a fixed arrow of time, and requiring that field operators commute for spacelike distances. This procedure is questioned here in the context of quantum field theory in curved spacetime (QFTCS). In 1935, Einstein and Rosen (ER), in their seminal paper (Einstein and Rosen 1935
Phys. Rev.
48
73–77) proposed that ‘a particle in the physical Universe has to be described by mathematical bridges connecting two sheets of spacetime’ which involved two arrows of time. Recently proposed direct-sum quantum theory reconciles this ER’s vision by introducing geometric superselection sectors associated with the regions of spacetime related by discrete transformations. We further establish that the quantum effects at gravitational horizons involve the physics of quantum inverted harmonic oscillators that have phase space horizons. This new understanding of the ER bridges is not related to classical wormholes, it addresses the original ER puzzle and promises a unitary description of QFTCS, along with observer complementarity. Furthermore, we present compelling evidence for our new understanding of ER bridges in the form of large-scale parity asymmetric features in the cosmic microwave background, which is statistically 650 times stronger than the standard scale-invariant power spectrum from the typical understanding of inflationary quantum fluctuations when compared with the posterior probabilities associated with the model given the data. We finally discuss the implications of this new understanding in combining gravity and quantum mechanics.
The following article is
Open access
Interior-flat cylindrical nacelle warp bubbles: derivation and comparison with Alcubierre model
Harold White
et al
2025
Class. Quantum Grav.
42
235022
View article
, Interior-flat cylindrical nacelle warp bubbles: derivation and comparison with Alcubierre model
PDF
, Interior-flat cylindrical nacelle warp bubbles: derivation and comparison with Alcubierre model
We present a new class of warp bubble geometries that are both interior-flat and segmented into Gaussian cylinders (interchangeably called ‘nacelles’
throughout the paper), providing an alternative to the continuous toroidal energy distribution of the Alcubierre model. Using the ADM 3+1 formalism, we derive the extrinsic curvature, York time, momentum densities, and energy density for both the Alcubierre baseline and the Gaussian cylinder generalizations with
cylinders equally spaced azimuthally around the warp bubble. The interior-flat condition guarantees that observers within the bubble remain synchronized with external clocks, yielding a habitable region of flat spacetime. Unlike the diffuse azimuthal ring of negative energy in the Alcubierre solution, our construction localizes exotic stress-energy into discrete cylindrical channels aligned with the bubble wall. Energy density maps, boost magnitude contours, and three-dimensional isosurfaces demonstrate how these segmented Gaussian cylinders maintain a synchronized interior while tuning curvature effects to end-caps. The results suggest that warp bubbles can be engineered with structurally discrete geometries resembling science-fiction starship architectures, where exotic matter localization, end-cap shaping, and interior flatness are tunable engineering parameters consistent with general relativity. These findings extend the ongoing search for physically motivated warp constructs and underscore the value of bridging theoretical warp metrics with engineering-oriented design principles.
The following article is
Open access
In the realm of the Hubble tension—a review of solutions
Eleonora Di Valentino
et al
2021
Class. Quantum Grav.
38
153001
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, In the realm of the Hubble tension—a review of solutions
PDF
, In the realm of the Hubble tension—a review of solutions
The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4
to 6
disagreement between predictions of the Hubble constant,
, made by the early time probes in concert with the ‘vanilla’ ΛCDM cosmological model, and a number of late time, model-independent determinations of
from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations—whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1–2
between
Planck
2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess,
et al
(2021
Astrophys. J.
908
L6) measurement of the Hubble constant (
= 73.2 ± 1.3 km s
−1
Mpc
−1
at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3
disagreement level. In many cases, reduced tension comes not simply from a change in the value of
but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.
The following article is
Open access
Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
Sunny Vagnozzi
et al
2023
Class. Quantum Grav.
40
165007
View article
, Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
PDF
, Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical general relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A
(Sgr A
), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A
’s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A
places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A
and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well-motivated alternative scenarios, including BH mimickers, are far from being ruled out at present.
The following article is
Open access
A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals
B P Abbott
et al
2020
Class. Quantum Grav.
37
055002
View article
, A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals
PDF
, A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals
The LIGO Scientific Collaboration and the Virgo Collaboration have cataloged eleven confidently detected gravitational-wave events during the first two observing runs of the advanced detector era. All eleven events were consistent with being from well-modeled mergers between compact stellar-mass objects: black holes or neutron stars. The data around the time of each of these events have been made publicly available through the gravitational-wave open science center. The entirety of the gravitational-wave strain data from the first and second observing runs have also now been made publicly available. There is considerable interest among the broad scientific community in understanding the data and methods used in the analyses. In this paper, we provide an overview of the detector noise properties and the data analysis techniques used to detect gravitational-wave signals and infer the source properties. We describe some of the checks that are performed to validate the analyses and results from the observations of gravitational-wave events. We also address concerns that have been raised about various properties of LIGO–Virgo detector noise and the correctness of our analyses as applied to the resulting data.
The following article is
Open access
Life on a closed timelike curve
L Gavassino 2025
Class. Quantum Grav.
42
015002
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, Life on a closed timelike curve
PDF
, Life on a closed timelike curve
We study the internal dynamics of a hypothetical spaceship traveling on a close timelike curve in an axially symmetric Universe. We choose the curve so that the generator of evolution in proper time is the angular momentum. Using Wigner’s theorem, we prove that the energy levels internal to the spaceship must undergo spontaneous discretization. The level separation turns out to be finely tuned so that, after completing a roundtrip of the curve, all systems are back to their initial state. This implies, for example, that the memories of an observer inside the spaceship are necessarily erased by the end of the journey. More in general, if there is an increase in entropy, a Poincaré cycle will eventually reverse it by the end of the loop, forcing entropy to decrease back to its initial value. We show that such decrease in entropy is in agreement with the eigenstate thermalization hypothesis. The non-existence of time-travel paradoxes follows as a rigorous corollary of our analysis.
The following article is
Open access
Pulsar timing arrays-challenges, and current status
G M Shaifullah 2025
Class. Quantum Grav.
42
243001
View article
, Pulsar timing arrays-challenges, and current status
PDF
, Pulsar timing arrays-challenges, and current status
This review summarises recent progress in pulsar timing array research and the current status of nanohertz gravitational wave astronomy. I outline the techniques enabling decade-long, sub-microsecond-precision timing, present results from PTA collaborations between 2023–2025, and discuss their implications for supermassive black-hole binaries, cosmological sources, and beyond-Standard-Model physics. I also highlight complimentary efforts probing the nanohertz regime.
The following article is
Open access
Validation of optical pathlength stability in a LISA test-bench demonstrator
Shivani Harer
et al
2026
Class. Quantum Grav.
43
075001
View article
, Validation of optical pathlength stability in a LISA test-bench demonstrator
PDF
, Validation of optical pathlength stability in a LISA test-bench demonstrator
The Laser Interferometer Space Antenna (LISA) observatory is a future L3 mission of the European Space Agency to detect gravitational waves, set to launch in 2035. The detector constellation will conduct interferometry to extreme precision over an unprecedented armlength of 2.5 million kms. In this paper, we present the development and testing results for the Zerodur interferometer (ZIFO), an optical demonstrator built to validate critical technology for the test setup of LISA’s interferometric core. Optical pathlength stability measurements on the ZIFO demonstrate successful reduction of bench noise to maintain the 10 pm
specification across the 1 mHz to 1 Hz frequency band. We also identify and characterize dominant noise sources from phasemeters and correlations of beam tilt into the pathlength that are observed during the test campaign.
The following article is
Open access
Gravitational lensing beyond the eikonal approximation
Emma Bruyère and Cyril Pitrou 2026
Class. Quantum Grav.
43
085010
View article
, Gravitational lensing beyond the eikonal approximation
PDF
, Gravitational lensing beyond the eikonal approximation
Waves propagating through a gravitational potential exhibit wave-optics effects when their wavelength is not significantly smaller than the lensing scales. We study the propagation of a scalar wave, governed by the Klein–Gordon equation in curved spacetime, to focus on effects on amplitude and phase, while leaving aside the issue of wave polarization which affects electromagnetic and gravitational waves. Using the Newman–Penrose formalism, we obtain the first corrections beyond the geometric optics in the expansion in the inverse frequency. In vacuum, that is for Weyl tensor lensing, there is no wave effect at first order in
and wave effects start at order
. Conversely, if the wave travels through a non-vanishing matter density, the first corrections start at order
. We check these analytic results by solving numerically the equations dictating the evolution of the corrections either in the vicinity of a Schwarzschild black hole or through a transparent star.
Finite curvature construction of regular black holes and quasinormal mode analysis
Chen Lan
et al
2026
Class. Quantum Grav.
43
085009
View article
, Finite curvature construction of regular black holes and quasinormal mode analysis
PDF
, Finite curvature construction of regular black holes and quasinormal mode analysis
We develop a class of regular black holes by prescribing finite curvature invariants and reconstructing the corresponding spacetime geometry. Two distinct approaches are employed: one based on the Ricci scalar and the other on the Weyl scalar. In each case, we explore a variety of analytic profiles for the curvature functions, including Gaussian, hyperbolic secant, and rational forms, ensuring regularity, asymptotic flatness, and compatibility with dominant energy conditions. The resulting mass functions yield spacetime geometries free from curvature singularities and exhibit horizons depending on model parameters. To assess the stability of these solutions, we perform a detailed analysis of quasinormal modes (QNMs) under axial gravitational perturbations. We show that the shape of the effective potential, particularly its width and the presence of potential valleys, plays a critical role in determining the QNMs. Models with a large peak-to-valley ratio in the potential barrier tend to support longer-lived oscillations, since perturbations can be partially trapped in the valley region before eventually escaping. By contrast, when the ratio is small, the valley is too shallow to produce effective trapping, and the waveforms reduce to standard exponential decay without sustained oscillatory behavior. Our results highlight the significance of potential design in constructing physically viable and dynamically stable regular black holes, offering potential observational implications in modified gravity and quantum gravity scenarios.
The globally trapped future: a fate for black holes and wormholes
Yi-Bo Liang and Hong-Rong Li 2026
Class. Quantum Grav.
43
08LT01
View article
, The globally trapped future: a fate for black holes and wormholes
PDF
, The globally trapped future: a fate for black holes and wormholes
We present a novel framework that can generate any spherically symmetric metric (at least locally) through a coupled scalar-electromagnetic system. We then specialize to a class of non-stationary spacetimes characterized by analytically tractable global causal structure and trapping horizons, which is particularly suited for investigating the evolution of black holes and wormholes. Within this framework, we find that the fate of spacetime can be categorized into three distinct classes: those without a globally trapped future; those without a globally trapped future but containing bounded, Cauchy-foliated trapped regions; and those with a future that becomes completely trapped. The evolution of a geometrically Schwarzschild-like black hole and a horizonless wormhole demonstrates these possible fates, thus revealing the globally trapped outcome as a novel theoretical possibility. Finally, we propose that a regular black hole may contain an unattainable minimal throat—a minimal-radius throat that is causally unreachable—and refer to it henceforth as the asymptotic throat.
The following article is
Open access
Impact of facility timing and coordination for next-generation gravitational-wave detectors
Ssohrab Borhanian
et al
2026
Class. Quantum Grav.
43
085008
View article
, Impact of facility timing and coordination for next-generation gravitational-wave detectors
PDF
, Impact of facility timing and coordination for next-generation gravitational-wave detectors
While the Einstein telescope and cosmic explorer proposals for next-generation (XG), ground-based detectors promise vastly improved sensitivities to gravitational-wave signals, only joint observations are expected to enable the full scientific potential of these facilities, making timing and coordination between the efforts crucial to avoid missed opportunities. This study investigates the impact of long-term delays on the scientific capabilities of XG detector networks. We use the Fisher information formalism to simulate the performance of a set of detector networks for large, fiducial populations of binary black holes, binary neutron stars, and primordial black-hole binaries. Bootstrapping the simulated populations, we map the expected observation times required to reach a number of observations fulfilling scientific targets for key sensitivity and localization metrics across various network configurations. We also investigate the sensitivity to stochastic backgrounds. We find that purely sensitivity-driven metrics such as the signal-to-noise ratio are not strongly affected by delays between facilities. This is contrasted by the localization metrics, which are very sensitive to the number of detectors in the network and, by extension, to delayed observation campaigns for a detector. Effectively, delays in one detector behave like network-wide interruptions for the localization metrics for networks consisting of two XG facilities. We examine the impact of a supporting, current-generation detector such as LIGO India operating concurrently with XG facilities and find such an addition will greatly mitigate the negative effects of delays for localization metrics, with important consequences on multi-messenger science and stochastic searches.
Curvature corrections to the Yukawa potential in Tolman metrics
J V Zamperlini and C C Barros Jr 2026
Class. Quantum Grav.
43
085007
View article
, Curvature corrections to the Yukawa potential in Tolman metrics
PDF
, Curvature corrections to the Yukawa potential in Tolman metrics
This work investigates curvature-induced modifications to the Yukawa potential in static, spherically symmetric spacetimes described by Tolman metrics, focusing on their implications for compact stellar objects, with particular application to solutions IV and VI. Motivated by the interplay of quantum interactions and strong gravitational fields in systems like neutron stars, we derive explicit corrections to the Yukawa potential for these metrics based on recent work. Revisiting the previous result, contrary to what was found, that curvature corrections break the interacting potential radial symmetry near a highly charged black hole, we show that Tolman metric corrections still provide the same symmetry in the local inertial frame. Numerical estimates for astrophysical objects reveal energy shifts of the order of
for the solution IV. The Tolman VI solution, while singular at the center, yields comparable corrections for most of the fluid sphere radius. A detailed analysis of the repulsive or attractive feature of the curvature corrections for a local observer is done for each scenario. Despite providing small corrections, these results highlight the role of spacetime geometry in shaping quantum interactions and provide a foundation for future studies of nuclear interactions within the context of relativistic stars.
Ten years of extreme gravity tests of general theory of relativity with gravitational-wave observations
Anuradha Gupta 2026
Class. Quantum Grav.
43
053001
View article
, Ten years of extreme gravity tests of general theory of relativity with gravitational-wave observations
PDF
, Ten years of extreme gravity tests of general theory of relativity with gravitational-wave observations
Ten years ago, the first direct detection of gravitational waves (GWs) from the merger of two black holes, GW150914, provided the very first opportunity to test Einstein’s general theory of relativity (GR) in the extreme gravity regime, where the gravitational field is strong, characteristic speeds are highly relativistic, and spacetime is dynamical. Such a regime is currently accessible only through coalescing compact binaries. In this review, we summarize the status of testing GR with GW observations and discuss the lessons learned. We also touch upon the challenges we currently have in testing GR and the potential path forward to detect a credible violation of GR, should one exist in the data.
The following article is
Open access
Using gravitational waves & multi-messenger astronomy to reverse-engineer the properties of galactic nuclei
K E Saavik Ford and Barry McKernan 2026
Class. Quantum Grav.
43
033001
View article
, Using gravitational waves & multi-messenger astronomy to reverse-engineer the properties of galactic nuclei
PDF
, Using gravitational waves & multi-messenger astronomy to reverse-engineer the properties of galactic nuclei
Active galactic nuclei (AGN) are powered by accretion disks onto supermassive black holes (SMBHs) in the centers of galaxies. AGN are believed to play important roles in the evolution of both SMBHs and their host galaxies over cosmic time. AGN and the nuclear star clusters (NSCs) that interact with them remain unresolved with present and planned telescopes. As a result, the properties of AGN and NSCs are highly uncertain. Here we review how binary black hole (BBH) mergers can occur in AGN disks and how both the gravitational wave and electromagnetic wave properties of such mergers allow us to reverse-engineer the properties of AGN disks and NSCs over cosmic time. We point out that the feature in the BBH mass spectrum around
is an excellent probe of hierarchical merger models. Likewise constraints on the spins of upper-mass gap BH (
) test the AGN channel. The effective spin (
) distribution, including asymmetry, islands of structure and magnitudes are excellent tests of AGN model predictions. We also argue, that the rate of AGN-driven BBH mergers as a function of redshift should scale slightly shallower than the AGN number density, at least out to redshifts of
, and should turnover at the same redshift as the AGN number density. Finally, we emphasize a determination of an AGN fraction of observed BBH mergers (
),
regardless of the actual value
, allows us to infer the average properties of AGN disks and NSCs out to high redshift.
The following article is
Open access
Pulsar timing arrays-challenges, and current status
G M Shaifullah 2025
Class. Quantum Grav.
42
243001
View article
, Pulsar timing arrays-challenges, and current status
PDF
, Pulsar timing arrays-challenges, and current status
This review summarises recent progress in pulsar timing array research and the current status of nanohertz gravitational wave astronomy. I outline the techniques enabling decade-long, sub-microsecond-precision timing, present results from PTA collaborations between 2023–2025, and discuss their implications for supermassive black-hole binaries, cosmological sources, and beyond-Standard-Model physics. I also highlight complimentary efforts probing the nanohertz regime.
Progress of the TianQin project
Jun Luo
et al
2025
Class. Quantum Grav.
42
173001
View article
, Progress of the TianQin project
PDF
, Progress of the TianQin project
TianQin is a future space-based gravitational wave (GW) observatory targeting the frequency window of 10
−4
–1 Hz. A large variety of GW sources are expected in this frequency band, including the merger of massive black hole binaries, the inspiral of extreme/intermediate mass ratio systems, stellar-mass black hole binaries, Galactic compact binaries, and so on. TianQin will consist of three Earth orbiting satellites on nearly identical orbits with orbital radii of about 10
km. The satellites will form a normal triangle constellation whose plane is nearly perpendicular to the ecliptic plane. The TianQin project has been progressing smoothly following the ‘0123’ technology roadmap. In step ‘0’, the TianQin laser ranging station has been constructed and it has successfully ranged to all the five retro-reflectors on the Moon. In step ‘1’, the drag-free control technology has been tested and demonstrated using the TianQin-1 satellite. In step ‘2’, the inter-satellite laser interferometry technology will be tested using the pair of TianQin-2 satellites. The TianQin-2 mission has been officially approved and the satellites will be launched around 2026. In step ‘3’, i.e. the TianQin-3 mission, three identical satellites will be launched around 2035 to form the space-based GW detector, TianQin, and to start GW detection in space.
Gravitational wave tails from soft theorem: a short review
Ashoke Sen 2025
Class. Quantum Grav.
42
143002
View article
, Gravitational wave tails from soft theorem: a short review
PDF
, Gravitational wave tails from soft theorem: a short review
If a set of massive objects collide in space and the fragments disperse, possibly forming black holes, then this process will emit gravitational waves. Computing the detailed gravitational wave-form associated with this process is a complicated problem, not only due to the non-linearity of gravity but also due to the fact that during the collision and subsequent fragmentation the objects could undergo complicated non-gravitational interactions. Nevertheless the classical soft graviton theorem determines the power law fall-off of the wave-form at late and early times, including logarithmic corrections, in terms of only the momenta of the incoming and outgoing objects without any reference to what transpired during the collision. In this short review I shall explain the results and very briefly outline the derivation of these results.
The following article is
Open access
Holographic pressure and volume for black holes
Borsboom et al
View accepted manuscript
, Holographic pressure and volume for black holes
PDF
, Holographic pressure and volume for black holes
We advocate for a holographic definition of thermodynamic pressure and volume for black holes based on quasi-local gravitational thermodynamics. When a black hole is enclosed by a finite timelike boundary, York's quasi-local first law includes a surface pressure conjugate to the boundary area. Assuming the existence of a holographically dual theory living on this boundary, these geometric quantities correspond to the pressure and volume of the dual thermal system. In this work we focus on static, spherically symmetric black holes, for which these quantities reduce to global thermodynamic variables. The holographic volume provides a notion of system size, allowing extensivity to be defined in standard thermodynamic terms, and it yields a definition of the large-system limit. For the asymptotically flat case, we show that, in the canonical thermodynamic representation, small Schwarzschild black holes are non-extensive, whereas large black holes become extensive in the large-system limit. A similar conclusion applies to Anti-de Sitter Schwarzschild black holes, with the difference that the quasi-local energy of the large black hole also becomes extensive in the large-system limit. Before this limit, the energy decomposes into subextensive and extensive contributions, and we derive an explicit expression for the extensive part as a function of the finite volume and entropy.
Husain-Kuchař model as the Carrollian limit of the Holst term
Fernando Barbero G et al
View accepted manuscript
, Husain-Kuchař model as the Carrollian limit of the Holst term
PDF
, Husain-Kuchař model as the Carrollian limit of the Holst term
We show how the Husain-Kuchař model can be understood as a Carrollian limit of the Holst term in the context of background-independent field theories described in terms of coframes and spin connections. We also discuss the footprint of the Carrollian symmetry in the Hamiltonian formulation of the Husain-Kuchař action.
Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
Blanchet et al
View accepted manuscript
, Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
PDF
, Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
We derive the gravitational radiation-reaction (RR) force in the harmonic coordinate system for general orbits in a general frame at the fourth-and-a-half post-Newtonian (4.5PN) order in the case of compact binary systems. Dimensional regularization is used to treat the ultra-violet divergences which appear at that order. We prove that the RR acceleration implies the known radiation fluxes at infinity associated with energy, angular momentum, linear momentum, and center-of-mass position. As a consistency check, we verify the manifest Lorentz invariance of the RR acceleration in harmonic coordinates. Our result should be useful for comparisons with other approaches such as the gravitational self force (GSF) and the post-Minkowskian (PM) expansion. In particular, it agrees with the recent 2PM derivation of the RR force using effective field theory.
The following article is
Open access
Asymptotic charges of a quadrupolar naked singularity
Gasperin et al
View accepted manuscript
, Asymptotic charges of a quadrupolar naked singularity
PDF
, Asymptotic charges of a quadrupolar naked singularity
The purpose of this article is to compute the asymptotic charges of a vacuum solution to the Einstein field equations describing a naked singularity with a non-vanishing quadrupole moment, known in the literature as the Zipoy-Voorhees spacetime (q-metric). In addition to the well-known asymptotic quantities such as the Bondi-Sachs energy-momentum, the BMS charges and NP constants of this spacetime are computed. Explicit calculations of the latter are relatively scarce in the literature. Moreover, it has been proven that the NP constants of asymptotically flat, stationary, vacuum, and algebraically special spacetimes vanish (for instance, those of the Kerr spacetime). A by-product of the present analysis is to show that the algebraically special condition in the aforementioned result appears to be crucial, since the q-metric provides a counterexample to the conjecture that all asymptotically flat, stationary, vacuum, and asymptotically algebraically special spacetimes (a weaker version of the algebraically special condition) have vanishing NP constants.
Revisiting Recent Progress in the Karch-Randall Braneworld
Geng
View accepted manuscript
, Revisiting Recent Progress in the Karch-Randall Braneworld
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, Revisiting Recent Progress in the Karch-Randall Braneworld
Motivated by the study of entanglement island in the Karch-Randall braneworld, it has been conjectured and proven in general that entanglement island is not consistent with long-range (massless) gravity. In this paper, we provide a careful check of this conclusion in a model of massless gravity that is constructed using the Karch-Randall braneworld. We show that there is indeed no entanglement island and hence not a nontrivial Page curve due to the diffeomorphism invariance if we are studying the correct question. We will also clarify the subtlety that is important to put this question in a correct manner. Moreover, we show that this conclusion is not affected by deforming the set-up with the Dvali-Gabadadze-Porrati (DGP) terms. Furthermore, we show that the consistency of holography in this model will provide nontrivial constraints to the DGP parameters. This study provides an example that causality and holography in anti-de Sitter space can be used to constrain low energy effective theories. We also clarify several subtleties in the braneworld gravity which were overlooked in the literature. We show that a direct implication of these clarifications is a resolution of the causality paradox in the Karch-Randall braneworld. At the end, we discuss the robustness of the above results against possible coarse-graining protocols to define a subregion in a gravitational theory. Contents 1 Introduction 1 2 No Entanglement Island in Massless Gravity 4 2.1 The Set-up 4 2.2 The Question and the Result without DGP Terms 5 2.3 Adding DGP Terms Doesn't Change the Result 8 2.4 A Question in the Boundary Description 9 3 Consistency of Wedge Holography and the Swampland Bounds 10 4 The Intermediate Picture and Coarse-Graining 11 4.1 The Precise Description of the Intermediate Picture 12 4.2 An Implication-Resolution of the Causality Paradox 15 4.3 The Derivation of the Modified Island Formula 19 4.4 A Potential Puzzle and Its Resolution 21 4.5 Robustness of the Result Under Coarse Graining 22 5 Conclusion 23
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Gravitational lensing beyond the eikonal approximation
Emma Bruyère and Cyril Pitrou 2026
Class. Quantum Grav.
43
085010
View article
, Gravitational lensing beyond the eikonal approximation
PDF
, Gravitational lensing beyond the eikonal approximation
Waves propagating through a gravitational potential exhibit wave-optics effects when their wavelength is not significantly smaller than the lensing scales. We study the propagation of a scalar wave, governed by the Klein–Gordon equation in curved spacetime, to focus on effects on amplitude and phase, while leaving aside the issue of wave polarization which affects electromagnetic and gravitational waves. Using the Newman–Penrose formalism, we obtain the first corrections beyond the geometric optics in the expansion in the inverse frequency. In vacuum, that is for Weyl tensor lensing, there is no wave effect at first order in
and wave effects start at order
. Conversely, if the wave travels through a non-vanishing matter density, the first corrections start at order
. We check these analytic results by solving numerically the equations dictating the evolution of the corrections either in the vicinity of a Schwarzschild black hole or through a transparent star.
The following article is
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Holographic pressure and volume for black holes
Silvester G.A. Borsboom and Manus Visser 2026
Class. Quantum Grav.
View article
, Holographic pressure and volume for black holes
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, Holographic pressure and volume for black holes
We advocate for a holographic definition of thermodynamic pressure and volume for black holes based on quasi-local gravitational thermodynamics. When a black hole is enclosed by a finite timelike boundary, York's quasi-local first law includes a surface pressure conjugate to the boundary area. Assuming the existence of a holographically dual theory living on this boundary, these geometric quantities correspond to the pressure and volume of the dual thermal system. In this work we focus on static, spherically symmetric black holes, for which these quantities reduce to global thermodynamic variables. The holographic volume provides a notion of system size, allowing extensivity to be defined in standard thermodynamic terms, and it yields a definition of the large-system limit. For the asymptotically flat case, we show that, in the canonical thermodynamic representation, small Schwarzschild black holes are non-extensive, whereas large black holes become extensive in the large-system limit. A similar conclusion applies to Anti-de Sitter Schwarzschild black holes, with the difference that the quasi-local energy of the large black hole also becomes extensive in the large-system limit. Before this limit, the energy decomposes into subextensive and extensive contributions, and we derive an explicit expression for the extensive part as a function of the finite volume and entropy.
The following article is
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Asymptotic charges of a quadrupolar naked singularity
Edgar Gasperin and Mariem Magdy 2026
Class. Quantum Grav.
View article
, Asymptotic charges of a quadrupolar naked singularity
PDF
, Asymptotic charges of a quadrupolar naked singularity
The purpose of this article is to compute the asymptotic charges of a vacuum solution to the Einstein field equations describing a naked singularity with a non-vanishing quadrupole moment, known in the literature as the Zipoy-Voorhees spacetime (q-metric). In addition to the well-known asymptotic quantities such as the Bondi-Sachs energy-momentum, the BMS charges and NP constants of this spacetime are computed. Explicit calculations of the latter are relatively scarce in the literature. Moreover, it has been proven that the NP constants of asymptotically flat, stationary, vacuum, and algebraically special spacetimes vanish (for instance, those of the Kerr spacetime). A by-product of the present analysis is to show that the algebraically special condition in the aforementioned result appears to be crucial, since the q-metric provides a counterexample to the conjecture that all asymptotically flat, stationary, vacuum, and asymptotically algebraically special spacetimes (a weaker version of the algebraically special condition) have vanishing NP constants.
The following article is
Open access
Impact of facility timing and coordination for next-generation gravitational-wave detectors
Ssohrab Borhanian
et al
2026
Class. Quantum Grav.
43
085008
View article
, Impact of facility timing and coordination for next-generation gravitational-wave detectors
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, Impact of facility timing and coordination for next-generation gravitational-wave detectors
While the Einstein telescope and cosmic explorer proposals for next-generation (XG), ground-based detectors promise vastly improved sensitivities to gravitational-wave signals, only joint observations are expected to enable the full scientific potential of these facilities, making timing and coordination between the efforts crucial to avoid missed opportunities. This study investigates the impact of long-term delays on the scientific capabilities of XG detector networks. We use the Fisher information formalism to simulate the performance of a set of detector networks for large, fiducial populations of binary black holes, binary neutron stars, and primordial black-hole binaries. Bootstrapping the simulated populations, we map the expected observation times required to reach a number of observations fulfilling scientific targets for key sensitivity and localization metrics across various network configurations. We also investigate the sensitivity to stochastic backgrounds. We find that purely sensitivity-driven metrics such as the signal-to-noise ratio are not strongly affected by delays between facilities. This is contrasted by the localization metrics, which are very sensitive to the number of detectors in the network and, by extension, to delayed observation campaigns for a detector. Effectively, delays in one detector behave like network-wide interruptions for the localization metrics for networks consisting of two XG facilities. We examine the impact of a supporting, current-generation detector such as LIGO India operating concurrently with XG facilities and find such an addition will greatly mitigate the negative effects of delays for localization metrics, with important consequences on multi-messenger science and stochastic searches.
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Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities
Pavan Chawhan
et al
2026
Class. Quantum Grav.
View article
, Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities
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, Axisymmetric hydrodynamics in numerical relativity: treating coordinate singularity, artificial heating and modeling MHD instabilities
Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on ~10
ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.
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Quantum-Gravitational Backreaction in theBTZ Background from Curved MomentumSpace
Partha Nandi
et al
2026
Class. Quantum Grav.
View article
, Quantum-Gravitational Backreaction in theBTZ Background from Curved MomentumSpace
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, Quantum-Gravitational Backreaction in theBTZ Background from Curved MomentumSpace
We explore how quantum properties of spacetime—specifically the curvature of momentum space—can backreact on classical gravity within a tractable semiclassical $(2+1)$-dimensional framework with negative cosmological constant. Motivated by quantum-gravity scenarios, we investigate how Planck-scale modifications of particle kinematics influence both dynamics and gravitational solutions. Starting from a first-order action, we derive an effective configuration-space description and show that particle trajectories remain geodesic, preserving the weak equivalence principle despite the underlying deformation. Coupling this modified matter sector to Einstein gravity, we obtain a deformed BTZ black hole solution. Remarkably, the local geometric structure and thermodynamic relations retain their standard form, while all quantum-gravity effects are encoded in a nonlinear mapping between the microscopic mass parameter and the ADM mass. This induces a renormalization of the horizon radius and thermodynamic quantities without altering their functional dependence. As a concrete observable consequence, we compute corrections to the return time of massless probes traveling along null geodesics between the horizon and the $AdS_3$ boundary. Our results demonstrate that Planck-scale kinematic effects can leave controlled and potentially measurable imprints on classical geometry, providing a clear and consistent bridge between quantum gravity ideas and semiclassical observables.
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Characteristic First-Order Structure of f(R) Gravity in Spherical Symmetry
Philippe G LeFloch and Filipe C Mena 2026
Class. Quantum Grav.
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, Characteristic First-Order Structure of f(R) Gravity in Spherical Symmetry
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, Characteristic First-Order Structure of f(R) Gravity in Spherical Symmetry
We develop an augmented characteristic, first-order formulation of the field equations in f(R) gravity governing the global evolution of a (possibly) massive scalar field $\phi$ under spherical symmetry. This formulation is designed to isolate the genuine dynamical degrees of freedom while preserving the geometric structure of the theory. By treating the spacetime scalar curvature as an independent unknown, we obtain a closed first-order nonlocal system for the pair (\phi,R). This augmentation eliminates the higher-derivative character of the original equations at the level of the principal part. Our formulation allows us to pose the characteristic initial value problem and to establish several structural properties of solutions. More precisely, we work in generalized Bondi–Sachs coordinates and prescribe initial data on an asymptotically flat future light cone with vertex at the center of symmetry, and we identify the minimal regularity conditions required at the center. These regularity conditions are shown to be precisely those ensuring equivalence between the reduced system and the full f(R) equations. Extending Christodoulou’s method for the Einstein–scalar-field system, we recast the f(R) field equations as an integro-differential system of two coupled, first-order, nonlocal, nonlinear hyperbolic equations, whose principal unknowns are the scalar field and the spacetime scalar curvature. In deriving this reduced two-equation system, we impose natural assumptions on the scalar-field potential and on the function f(R) governing the gravitational Lagrangian density. These hypotheses correspond to standard viability and positivity conditions commonly imposed in the f(R) literature. We prove several equivalence and monotonicity properties, including for the Hawking mass in this setting.The proposed formulation separates the essential null evolution from the radial constraint reconstruction (via explicit integral relations) on the future domain of dependence of the initial light cone. This structure makes the system amenable to characteristic energy estimates and to stable numerical implementation in spherical symmetry.
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Investigation of Electrostatic Force and Acceleration Noise in Test Mass Caused by the Patch Effect
Wenke Shi
et al
2026
Class. Quantum Grav.
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, Investigation of Electrostatic Force and Acceleration Noise in Test Mass Caused by the Patch Effect
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, Investigation of Electrostatic Force and Acceleration Noise in Test Mass Caused by the Patch Effect
This study focuses on test-mass (TM) noise induced by the patch effect in space-borne gravitational-wave detection, through systematic theoretical and experimental analyses. Based on a two-dimensional quasi-local correlation model and the structural parameters of the TianQin and LISA missions, we calculate the electrostatic forces generated by multi-scale patch potentials. The results indicate that the system operates in the transition region (a/w ∼ 10) under practical working conditions, with an actual working gap of 4 mm and a typical patch size of 0.4 mm. Scanning Kelvin Probe Force Microscopy (KPFM) was employed to characterize the spatiotemporal distribution of surface potentials on gold-plated films, yielding a potential standard deviation of 15.61 mV and a potential noise amplitude spectral density of approximately 21. The results quantify the specific impact of the patch effect on both missions: electrostatic forces range from 10-12 to 10-14 N, and the acceleration noise at 1 mHz is approximately 1.24×10-16. Maintaining the surface potential standard deviation below 10 mV across the entire frequency band can meet the theoretical requirement of 3×10-16. Finally, noise-suppression strategies based on structural design and surface-process optimization are proposed, providing a foundation for improving payload performance in space-based gravitational-wave detection. These results provide a foundation for payload performance improvement in space-based gravitational-wave detection and establish a unified, mission-oriented, experimentally supported framework for evaluating patch-effect-induced electrostatic forces and acceleration noise.
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Disentangling spinning and nonspinning binary black hole populations with spin sorting
Lillie Szemraj and Sylvia Biscoveanu 2026
Class. Quantum Grav.
43
085005
View article
, Disentangling spinning and nonspinning binary black hole populations with spin sorting
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, Disentangling spinning and nonspinning binary black hole populations with spin sorting
The individual component spins of binary black holes (BBHs) are difficult to resolve using gravitational-wave observations but carry key signatures of the processes shaping their formation and evolution. Recent analyses have found conflicting evidence for a sub-population of black holes with negligible spin, but the
Default
spin magnitude population model used in LIGO-Virgo-KAGRA analyses cannot formally accommodate an excess of systems with zero spin. In this work, we analyze several different simulated BBH populations to demonstrate that even in the face of this mismodeling, spinning and nonspinning populations can be reliably distinguished using the
Default
spin magnitude population model coupled with spin sorting. While typical analyses sort the binary components by their masses, sorting the components by their spin magnitudes instead offers a complementary view of the properties of individual systems consistent with equal mass and of population-level properties, given binary evolution processes like tidal-spin up that predict asymmetric spin magnitudes among the binary components. We conclude that current observations of the BBH population are inconsistent with a fully nonspinning population, but could be explained by a population with only one spinning black hole per binary or a population with up to
nonspinning sources.
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Open access
Long short-term memory for early warning detection of gravitational waves
Reem Alfaidi and Christopher Messenger 2026
Class. Quantum Grav.
43
085003
View article
, Long short-term memory for early warning detection of gravitational waves
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, Long short-term memory for early warning detection of gravitational waves
Pre-merger detection of gravitational waves during the early inspiral of compact binary coalescences would enable electromagnetic observations of the earliest merger stages. This would significantly impact multi-messenger astronomy, giving astronomers potential access to rich new information. Here, we introduce a proof-of-concept deep-learning-based approach to produce early-warning alerts for binary black hole systems. We show the possibility of using a long short-term memory network trained on the whitened detector strain in the time domain to detect and classify compact binary events. In this work, we consider a single advanced laser interferometer gravitational-wave observatory detector at design sensitivity and make approximate sensitivity and early warning capability comparisons with approximations to traditional matched filtering approaches. We find that our model is competitive in both aspects, and when applied to a simulated test dataset was able to produce an early alert up to 5.3 s before the merger at a fixed false-alarm rate of one per day. These results demonstrate the feasibility of lightweight, low-latency recurrent neural networks for rapid gravitational-wave discovery, providing a pathway toward real-time early-warning systems for multi-messenger follow-up. This proof-of-concept in Gaussian noise for a single detector is readily extendable to real multi-detector observations.
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Advanced LIGO
The LIGO Scientific Collaboration
et al
2015
Class. Quantum Grav.
32
074001
View article
, Advanced LIGO
PDF
, Advanced LIGO
The Advanced LIGO gravitational wave detectors are second-generation instruments designed and built for the two LIGO observatories in Hanford, WA and Livingston, LA, USA. The two instruments are identical in design, and are specialized versions of a Michelson interferometer with 4 km long arms. As in Initial LIGO, Fabry–Perot cavities are used in the arms to increase the interaction time with a gravitational wave, and power recycling is used to increase the effective laser power. Signal recycling has been added in Advanced LIGO to improve the frequency response. In the most sensitive frequency region around 100 Hz, the design strain sensitivity is a factor of 10 better than Initial LIGO. In addition, the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have been replaced with improved technologies to achieve this sensitivity gain. Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power, larger test masses and improved mirror coatings lead to the improved sensitivity at mid and high frequencies. Data collecting runs with these new instruments are planned to begin in mid-2015.
TianQin: a space-borne gravitational wave detector
Jun Luo
et al
2016
Class. Quantum Grav.
33
035010
View article
, TianQin: a space-borne gravitational wave detector
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, TianQin: a space-borne gravitational wave detector
TianQin is a proposal for a space-borne detector of gravitational waves in the millihertz frequencies. The experiment relies on a constellation of three drag-free spacecraft orbiting the Earth. Inter-spacecraft laser interferometry is used to monitor the distances between the test masses. The experiment is designed to be capable of detecting a signal with high confidence from a single source of gravitational waves within a few months of observing time. We describe the preliminary mission concept for TianQin, including the candidate source and experimental designs. We present estimates for the major constituents of the experiment’s error budget and discuss the project’s overall feasibility. Given the current level of technological readiness, we expect TianQin to be flown in the second half of the next decade.
Advanced Virgo: a second-generation interferometric gravitational wave detector
F Acernese
et al
2015
Class. Quantum Grav.
32
024001
View article
, Advanced Virgo: a second-generation interferometric gravitational wave detector
PDF
, Advanced Virgo: a second-generation interferometric gravitational wave detector
Advanced Virgo is the project to upgrade the Virgo interferometric detector of gravitational waves, with the aim of increasing the number of observable galaxies (and thus the detection rate) by three orders of magnitude. The project is now in an advanced construction phase and the assembly and integration will be completed by the end of 2015. Advanced Virgo will be part of a network, alongside the two Advanced LIGO detectors in the US and GEO HF in Germany, with the goal of contributing to the early detection of gravitational waves and to opening a new window of observation on the universe. In this paper we describe the main features of the Advanced Virgo detector and outline the status of the construction.
The following article is
Open access
In the realm of the Hubble tension—a review of solutions
Eleonora Di Valentino
et al
2021
Class. Quantum Grav.
38
153001
View article
, In the realm of the Hubble tension—a review of solutions
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, In the realm of the Hubble tension—a review of solutions
The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4
to 6
disagreement between predictions of the Hubble constant,
, made by the early time probes in concert with the ‘vanilla’ ΛCDM cosmological model, and a number of late time, model-independent determinations of
from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations—whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1–2
between
Planck
2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess,
et al
(2021
Astrophys. J.
908
L6) measurement of the Hubble constant (
= 73.2 ± 1.3 km s
−1
Mpc
−1
at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3
disagreement level. In many cases, reduced tension comes not simply from a change in the value of
but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.
The Einstein Telescope: a third-generation gravitational wave observatory
M Punturo
et al
2010
Class. Quantum Grav.
27
194002
View article
, The Einstein Telescope: a third-generation gravitational wave observatory
PDF
, The Einstein Telescope: a third-generation gravitational wave observatory
Advanced gravitational wave interferometers, currently under realization, will soon permit the detection of gravitational waves from astronomical sources. To open the era of precision gravitational wave astronomy, a further substantial improvement in sensitivity is required. The future space-based Laser Interferometer Space Antenna and the third-generation ground-based observatory Einstein Telescope (ET) promise to achieve the required sensitivity improvements in frequency ranges. The vastly improved sensitivity of the third generation of gravitational wave observatories could permit detailed measurements of the sources' physical parameters and could complement, in a multi-messenger approach, the observation of signals emitted by cosmological sources obtained through other kinds of telescopes. This paper describes the progress of the ET project which is currently in its design study phase.
Quasinormal modes of black holes and black branes
Emanuele Berti
et al
2009
Class. Quantum Grav.
26
163001
View article
, Quasinormal modes of black holes and black branes
PDF
, Quasinormal modes of black holes and black branes
Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.
The following article is
Open access
Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
Sunny Vagnozzi
et al
2023
Class. Quantum Grav.
40
165007
View article
, Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
PDF
, Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A
Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical general relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A
(Sgr A
), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A
’s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A
places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A
and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well-motivated alternative scenarios, including BH mimickers, are far from being ruled out at present.
Cosmological backgrounds of gravitational waves
Chiara Caprini and Daniel G Figueroa 2018
Class. Quantum Grav.
35
163001
View article
, Cosmological backgrounds of gravitational waves
PDF
, Cosmological backgrounds of gravitational waves
Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting proper definitions of GWs in flat space-time and in a cosmological setting (section 2). Following, we discuss the reasons why early universe GW backgrounds are of a stochastic nature, and describe the general properties of a stochastic background (section 3). We recap current observational constraints on stochastic backgrounds, and discuss the basic characteristics of present and future GW detectors, including advanced LIGO, advanced Virgo, the Einstein telescope, KAGRA, and LISA (section 4). We then review in detail early universe GW generation mechanisms, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation (section 5), GWs from processes that operate within extensions of the standard inflationary paradigm (section 6), GWs from post-inflationary preheating and related non-perturbative phenomena (section 7), GWs from first order phase transitions related or not to the electroweak symmetry breaking (section 8), and GWs from general topological defects, and from cosmic strings in particular (section 9). The phenomenology of these early universe processes is extremely rich, and some of the GW backgrounds they generate can be within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators.
Quintessence and black holes
V V Kiselev 2003
Class. Quantum Grav.
20
1187
View article
, Quintessence and black holes
PDF
, Quintessence and black holes
We present new static spherically symmetric exact solutions of the Einstein equations for quintessential matter surrounding a black hole, charged or uncharged, as well as for the case without a black hole. A condition of additivity and linearity in the energy–momentum tensor is introduced which allows one to obtain correct limits to known solutions for the electromagnetic static field, implying the relativistic relation between the energy density and pressure, as well as for the extraordinary case of the cosmological constant, i.e. de Sitter space. We classify the horizons, which evidently reveal themselves in static coordinates, and derive the Gibbons–Hawking temperatures. An example of quintessence with state parameter
= −2/3 is discussed in detail.
Sensitivity studies for third-generation gravitational wave observatories
S Hild
et al
2011
Class. Quantum Grav.
28
094013
View article
, Sensitivity studies for third-generation gravitational wave observatories
PDF
, Sensitivity studies for third-generation gravitational wave observatories
Advanced gravitational wave detectors, currently under construction, are expected to directly observe gravitational wave signals of astrophysical origin. The Einstein Telescope (ET), a third-generation gravitational wave detector, has been proposed in order to fully open up the emerging field of gravitational wave astronomy. In this paper we describe sensitivity models for ET and investigate potential limits imposed by fundamental noise sources. A special focus is set on evaluating the frequency band below 10 Hz where a complex mixture of seismic, gravity gradient, suspension thermal and radiation pressure noise dominates. We develop the most accurate sensitivity model, referred to as ET-D, for a third-generation detector so far, including the most relevant fundamental noise contributions.
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1984-present
Classical and Quantum Gravity
doi: 10.1088/issn.0264-9381
Online ISSN: 1361-6382
Print ISSN: 0264-9381