Classical Quantum Gravity Research Articles

Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

In this work, we consider a resonant bar detector of gravitational waves in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis (Class Quantum Gravity 37:195006, 2020). We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.

A rigidity theorem for asymptotically flat static manifolds and its applications

In this paper, we study the Minkowski-type inequality for asymptotically flat static manifolds ( M n , g ) (M^{n},g) with boundary and with dimension n > 8 n>8 that was established by McCormick [Proc. Amer. Math. Soc. 146 (2018), pp. 4039–4046]. First, we show that any asymptotically flat static ( M n , g ) (M^{n},g) which achieves the equality and has CMC or equipotential boundary is isometric to a rotationally symmetric region of the Schwarzschild manifold. Then, we apply conformal techniques to derive a new Minkowski-type inequality for the level sets of bounded static potentials. Taken together, these provide a robust approach to detecting rotational symmetry of asymptotically flat static systems. As an application, we prove global uniqueness of static metric extensions for the Bartnik data induced by both Schwarzschild coordinate spheres and Euclidean coordinate spheres in dimension n > 8 n > 8 under the natural condition of Schwarzschild stability. This generalizes an earlier result of Miao [Classical Quantum Gravity 22 (2005), pp. L53–L59]. We also establish uniqueness for equipotential photon surfaces with small Einstein-Hilbert energy. This is interesting to compare with other recent uniqueness results for static photon surfaces and black holes, e.g. see V. Agostiniani and L. Mazzieri [Comm. Math. Phys. 355 (2017), pp. 261–301], C. Cederbaum and G. J. Galloway [J. Math. Phys. 62 (2021), p. 22], and S. Raulot [Classical Quantum Gravity 38 (2021), p. 22].

Toward fixing a framework for conformal cyclic cosmology

Conformal Cyclic Cosmology (CCC) is a cyclic model of the universe put forward by Sir Roger Penrose (Cycles of Time: An Extraordinary New View of the Universe, Random House, Manhattan, 2010). A conformal invariance assumption in the neighbourhood of the crossover region between cycles (which Penrose calls aeons) allows successive space-times to be related by a conformal rescaling. A major open problem is how to choose the conformal factor in a unique way, and is a fundamental hurdle to further study. Proposals have been put forward by Newman (Gen Relativ Gravit 46(5):1–13, 2014), Tod (Gen Relativ Gravit 47(3):1–13, 2015) and Nurowski (Class Quantum Gravity 38(14):145004, 2021), but they disagree in one way or another with Penrose’s original assumptions as well as each other. In this paper we compare these different models in detail and rule out certain choices for the conformal factor that have been put forward by Penrose. We extend the results of Newman and fix inconsistencies that arose in his calculations. A new class of solutions are put forward which agree with Penrose’s assumptions exactly so long as a certain additional relation is satisfied.

Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin

We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany et al. [Classical Quantum Gravity 36, 075003 (2019)] and later Ramond [arXiv:2210.03866], a 12-dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the Mathisson-Papapetrou-Dixon equations of motion with the Tulczyjew-Dixon spin supplementary condition, to linear order in spin. We then perturb this system by adding the conservative pieces of the leading order gravitational self-force and self-torque sourced by the particle's mass and spin. We show that this perturbed system is Hamiltonian and derive expressions for the Hamiltonian function and symplectic form. This result extends a previous result for spinless point particles [F. M. Blanco and E. E. Flanagan, Phys. Rev. Lett. 130, 051201 (2023)].

Decomposable (5, 6)-solutions in eleven-dimensional supergravity

We present decomposable (5, 6)-solutions M̃1,4×M6 in eleven-dimensional supergravity by solving the bosonic supergravity equations for a variety of non-trivial flux forms. Many of the bosonic backgrounds presented here are induced by various types of null flux forms on products of certain totally Ricci-isotropic Lorentzian Walker manifolds and Ricci-flat Riemannian manifolds. These constructions provide an analogy of the work performed by Chrysikos and Galaev [Classical Quantum Gravity 37, 125004 (2020)], who made similar computations for decomposable (6, 5)-solutions. We also present bosonic backgrounds that are products of Lorentzian Einstein manifolds with a negative Einstein constant (in the “mostly plus” convention) and Riemannian Kähler–Einstein manifolds with a positive Einstein constant. This conclusion generalizes a result of Pope and van Nieuwenhuizen [Commun. Math. Phys. 122, 281–292 (1989)] concerning the appearance of six-dimensional Kähler–Einstein manifolds in eleven-dimensional supergravity. In this setting, we construct infinitely many non-symmetric decomposable (5, 6)-supergravity backgrounds by using the infinitely many Lorentzian Einstein–Sasakian structures with a negative Einstein constant on the 5-sphere, known from the work of Boyer et al. [Commun. Math. Phys. 262, 177–208 (2006)].

Non-spherical sources of Schwarzschild space-time

While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior) solutions to Einstein equations, which match smoothly on the boundary surface to the Schwarzschild (exterior) space-time, even though the fluid distribution is not endowed with spherical symmetry. The solutions are obtained by using the general approach outlined in Hernández-Pastora et al. (Class Quantum Gravity 33:235005, 2016), and satisfy the usual requirements imposed to any physically admissible interior solution. A discussion about the physical and geometric properties of the source is presented. The relativistic multipole moments (RMM) are explicitly calculated in terms of the physical variables, allowing to prove that spherical sources can only match to the Schwarzschild space-time. The complexity of the source is evaluated through the complexity factors. It is shown that there is only one independent complexity factor, as in the spherically symmetric case.

Gravitational potential in spherical topologies

We study the properties of the Newtonian gravitational potential in a spherical Universe for different topologies. For this, we use the non-Euclidean Newtonian theory developed in Vigneron [On non-Euclidean Newtonian theories and their cosmological backreaction, Classical Quantum Gravity 39, 155006 (2022)]. describing Newtonian gravitation in a spherical or hyperbolic Universe. The potential is calculated for a point mass in all the globally homogeneous regular spherical topologies, i.e., whose fundamental domain is unique and is a platonic solid. We provide the exact solution and the Taylor expansion series of the potential at a test position near the point mass. We show that the odd terms of the expansion can be interpreted as coming from the presence of a nonzero spatial scalar curvature, while the even terms relate to the closed nature of the topological space. A consequence is that, compared to the point mass solution in a 3-torus, widely used in Newtonian cosmological simulations, the spherical cases all feature an additional attractive first order term dependent solely on the spatial curvature. The choice of topology only affects the potential at second order and higher. For typical estimates of cosmological scales (curvature and topology), the strongest topological effect occurs in the case of the Poincar\'e dodecahedral space, but in general the effect of curvature dominates over topology. We also provide the set of equations that can be used to perform $N$-body simulations of structure formation in spherical topologies.

Can two ultrarelativistic objects lose almost all their energy to gravitational radiation?

In 2007, Pretorius and Khurana [Black hole mergers and unstable circular orbits, Classical Quantum Gravity 24, S83 (2007).] did ``speculate that at threshold [at a critical impact parameter], all of the kinetic energy of the system [two ultrarelativistic black holes] is converted to gravitational waves, which can be an arbitrarily large fraction of the total energy.'' However, in 2012, Sperhake et al. [Universality, Maximum Radiation and Absorption in High-Energy Collisions of Black Holes with Spin, Phys. Rev. Lett. 111, 041101 (2013).] performed numerical calculations that led them to the contrary conclusion: ``An extrapolation of our results to the limit $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$ suggests that about half of the center-of-mass energy of the system can be emitted in gravitational radiation, while the rest must be converted into rest-mass and spin energy.'' Here I present arguments against this latter conclusion and in support of the earlier speculation that for sufficiently large $\ensuremath{\gamma}$, all but an arbitrarily small fraction of the total energy can be radiated away as gravitational waves.

On Einstein–Born–Infeld conformally invariant theory

A new Weyl Born Infeld model is presented. It takes as basis the formalism for the mathematical description of conformal gravity based on the local twistor geometry from Merkulov (Class Quantum Gravity 1:349–354, 1984). As in the pure Maxwell case, the electromagnetic field can be naturally incorporated into this scheme by a modification of the local twistor parallel transport law. The dynamical equations of the linear case, namely the Bach equations for gravity and the Maxwell equations for the electromagnetic field, can not be obtained by varying a single quantity-the modified twistor connection, unless a geometric condition on a particular function of the invariants is imposed. When that condition is met, the Weyl–Maxwel gravity system are contained in the obtained set. The invariance under standard dualities and other generalized maps are briefly discussed.

Particle Motion under the Conservative Piece of the Self-Force is Hamiltonian.

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic, or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita etal. [Classical Quantum Gravity 34, 134001 (2017).CQGRDG0264-938110.1088/1361-6382/aa7342], which is valid only for nonresonant orbits.

Small solutions of the Einstein–Boltzmann-scalar field system with Bianchi symmetry

We show that small homogeneous solutions to the Einstein–Boltzmann-scalar field system exist globally toward the future and tend to the de Sitter solution in a suitable sense. More specifically, we assume that the spacetime is of Bianchi type I–VIII, that the matter is described by Israel particles and that there exists a scalar field with a potential which has a positive lower bound. This represents a generalization of the work [H. Lee and E. Nungesser, Classical Quantum Gravity 35, 025001 (2018)], where a cosmological constant was considered, and a generalization of [H. Lee and J. Lee, J. Math. Phys. 63, 031502 (2022)], where a spatially flat FLRW spacetime was considered. We obtain the global existence and asymptotic behavior of classical solutions to the Einstein–Boltzmann-scalar field system for small initial data.

Gauss-Bonnet black holes in ( 2+1 ) dimensions: Perturbative aspects and entropy features

We investigate some aspects of the ($2+1$)-dimensional Gauss-Bonnet black hole proposed in Hennigar et al. [Phys. Lett. B 808, 135657 (2020); Classical Quantum Gravity 38, 03LT01 (2021)]. The perturbations of scalar and massless spinorial fields are studied suggesting the dynamical stability of the geometry. The field evolution is analyzed calculating the quasinormal modes for different parameters and exploring the influence of the coupling constant of the theory. The hydrodynamical modes are also obtained in the small coupling limit. Furthermore, the entropy bound and the dominant semiclassical correction to the black hole entropy are calculated.

Testing Spacetime Orientability

Historically, a great deal of attention has been addressed to the question of what it would take to test experimentally the metrical structure of spacetime. Arguably, however, consideration of this question has been at the expense of comparable investigations into what it would take to test other structural features of spacetime. In this article, we critique and expand substantially upon an article by Hadley (Hadley in Class Quantum Gravity, 19:4565–4571, 2002), which constitutes one of the best-known paper-length studies of what it would take to test the orientability of spacetime. In so doing, we seek to clarify a number of matters which remain unclear in the wake of Hadley’s article, thereby allowing the literature on this topic to progress. More positively, we also present, compare, and evaluate a number of other potential approaches to testing the orientability of spacetime which have arisen in the recent physics literature.

Nonlinear Radiation Gauge for Near Kerr Spacetimes

In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by Chrzanowski in his work on metric reconstruction (Chrzanowski in Phys Rev D 11:2042–2062, 1975) on the Kerr background. It has been shown by Price et al. (Class Quantum Gravity 24:2367–2388, 2007) that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In (Andersson et al. Stability for linearized gravity on the Kerr spacetime, 2019), the ORG was used in proving linearized stability for the Kerr spacetime, and the new non-linear radiation gauge introduced here is a direct generalization of that gauge condition, and is intended to be used to study the stability of Kerr black holes under the evolution generated by the vacuum Einstein equation.

Unruh-DeWitt detectors in cosmological spacetimes

We analyze the response and thermal behavior of an Unruh-DeWitt detector as it travels through cosmological spacetimes, with special reference to the question of how to define surface gravity and temperature in dynamical spacetimes. Working within the quantum field theory on curved spacetime approximation, we consider a detector as it travels along geodesic and accelerated Kodama trajectories in de Sitter and asymptotically de Sitter FLRW spacetimes. By modelling the temperature of the detector using the detailed-balance form of the Kubo-Martin-Schwinger (KMS) conditions as it thermalizes, we can better understand the thermal behavior of the detector as it interacts with the quantum field, and use this to compare competing definitions of surface gravity and temperature that persist in the literature. These include the approaches of Kodama [Prog. Theor. Phys. 63, 1217 (1980).], Ashtekar and Krishnan [Living Rev. Relativity 7, 10 (2004).], Fodor et al. [Phys. Rev. D 54, 3882 (1996).], and Nielsen [Classical Quantum Gravity 23, 4637 (2006).]. While these are most often examined within the context of a dynamical black hole, here we shift focus to surface gravity on the evolving cosmological horizon.

About apparent superluminal drives in generic gravity theories

As is well known, there exists warp drives in GR, such as the Alcubierre bubbles, which achieve an apparent faster than light travel (Alcubierre in Class Quantum Gravity 11:L73, 1994). A result due to Gao and Wald (Class Quantum Gravity 17:4999, 2000) suggests that such a travel is unlikely for GR with matter satisfying both the Null Energy and the Null Generic Conditions. There exists a generalization of this statement due to Galloway, that ensures that the Gao–Wald result is true regardless the underlying gravity model, unless there exists at least one inextendible null geodesic with achronal image in the space time (a null line). The proof of this proposition is based on techniques of causal theories, and has never been released. In the present work an independent proof of this result is presented by use of the Raychaudhuri equation, and avoiding several technical complications described along the text. Some consequences of these affirmations are discussed at last section, in particular their potential use in problems of causality.

Whom actually do multipole moments belong to?

Using an integral definition given in Hernández-Pastora et al. (Class Quantum Gravity 33:225009, 2016) to calculate the relativistic multipole moments (RMM), and the ensuing generalized relativistic Gauss theorem, we prove that the evaluation of that volume integral in Erez–Rosen coordinates, leads to a specific link between the RMM and the source of the exterior space–time, provided we have a global static axisymmetric metric in that coordinate system for any Weyl exterior field. This result allows to establish a relationship between the RMM and certain volume integral expressions involving the material content of the source from its energy–momentum tensor as well as the interior metric. In particular the relativistic quadrupole moment for the Erez–Rosen space–time is obtained.

The effect of R\xe9nyi entropy on Hawking radiation

It is widely believed that Hawking radiation originates from excitations near the horizons of black holes (Hawking in Commun Math Phys 43:199, 1975, Giddings in Phys Lett B 754:39, 2016, Mathur in Class Quantum Gravity 26:224001, 2009). However, Giddings (Phys Lett B 754:39, 2016) proposed that the Hawking radiation spectrum that characterizes evaporating semi-classical black holes originates from a quantum “atmosphere”, which extends beyond the horizon of a black hole. Although several research projects have been conducted in this field, they have not yet taken into account the effect of Rényi entropy. In the present article, we will therefore consider the effect of Rényi entropy on Hawking radiation power. We assume that if the effect of Rényi entropy is very small, we suggest that the Hawking radiation should originate from the quantum “atmosphere” which extends beyond the black hole’s horizon for finite dimensions. That is, that Giddings’ suggestion is the more likely of the above possibilities. However, for infinite dimensions, both suggestions are equally credible. We briefly consider the very large effect of Rényi entropy on Hawking radiation power as well. We find that if the effect of Rényi entropy is very large and omega /T_{BH} is very small, then the power spectral density S_R is proportional to the power spectral density S_{BH}.

OUP accepted manuscript

Abstract We develop a new approach to find asymptotic symmetries in general relativity as a modification of the Lie-algebra-based approach proposed in T. Tomitsuka et al. [Classical Quantum Gravity 38, 225007 (2021)]. Those authors proposed an algorithmic protocol to investigate asymptotic symmetries. In particular, their guiding principle helps us to find a non-vanishing charge that generates an infinitesimal diffeomorphism. However, in order to check the integrability condition for the charges, it is necessary to solve differential equations to identify the integral curve of vector fields, which is usually quite hard. In this paper, we provide a sufficient condition of the integrability condition that can be checked without solving any differential equations, avoiding the difficulties in the approach in the above reference. As a demonstration, we investigate the asymptotic symmetries on a Killing horizon and find a new class of asymptotic symmetries. In 4D spacetimes with a spherical Killing horizon, we show that the algebra of the corresponding charges is a central extension of the algebra of vector fields.

Recent multimessenger constraints and the anisotropic neutron star

The impact of anisotropic pressure models in neutron stars (NSs) is increasing their compactness. Therefore, for the relatively soft NS equation of state (EOS), we can still obtain a relatively large maximum mass of NSs and a relatively short canonical NS radius. We systematically study the anisotropic NS properties using a refined EOS. We compare the results with the recent NS multimessenger constraints. We use a relativistic mean-field (RMF) model with the G3 parameter set to calculate the NS core EOSs. The standard SU(3) prescription and hyperon potential depths determine the hyperon coupling constants. We use the inner and outer crusts EOSs from Miyatsu et al. [Astrophys. J. 777, 4 (2013)]. We consider two kinds of EOSs at high densities: one with the maximum speed of sound in NS matter obeying the conformal bound, i.e., ${v}_{s}^{\mathrm{max}}=\frac{1}{\sqrt{3}}$ (WHSS) and one without considering this bound (WH). We have found for the WH EOS with $\mathrm{\ensuremath{\Delta}}=\ensuremath{-}1.8$ that NS properties predicted for an anisotropic NS based on the Horvat et al. model [Classical Quantum Gravity 28, 025009 (2011)] are entirely compatible with recent NS multimessenger constraints. Whether a $2.6{M}_{\ensuremath{\bigodot}}$ massive compact object observed in the GW190814 event is an anisotropic NS or not, we found that the compact object is not likely an anisotropic NS.