Class Of Gravity Theories Research Articles

Do regular quantum black holes exist?

Regular black holes do not exist in any classical theory of gravity including Einstein's general relativity. This unappealing feature is due to the appearance of a singularity in the interior of the black hole described by any classical theory. As Hawking argued, all known laws of physics must break down at the singularity. It is thus an important question whether this singularity can disappear in a quantum mechanical description of spacetime. In this letter, we therefore quantize the black hole interior in a Kantowski-Sachs minisuperspace representation in the presence of spontaneous Klein-Gordon matter field fluctuations. This leads to a Wheeler-DeWitt equation whose solution yields the interior wave function of the black hole. The regular part of this wave function satisfies the DeWitt boundary condition in that it vanishes at the singularity. Moreover, the wave function is regular and well behaved in the region around the singularity. These features of the wave function suggest that regular black holes do exist in quantum gravity.

How the non-metricity of the connection arises naturally in the classical theory of gravity

Spacetime geometry is described by two–a priori independent–geometric structures: the symmetric connection Γ and the metric tensor g. Metricity condition of Γ (i.e. ∇g = 0) is implied by the Palatini variational principle, but only when the matter fields belong to an exceptional class. In case of a generic matter field, Palatini implies non-metricity of Γ. Traditionally, instead of the (first order) Palatini principle, we use in this case the (second order) Hilbert principle, assuming metricity condition a priori. Unfortunately, the resulting right-hand side of the Einstein equations does not coincide with the matter energy-momentum tensor. We propose to treat seriously the Palatini-implied non-metric connection. The conventional Einstein’s theory, rewritten in terms of this object, acquires a much simpler and universal structure. This approach opens a room for the description of the large scale effects in General Relativity (dark matter?, dark energy?), without resorting to purely phenomenological terms in the Lagrangian of gravitational field. All theories discussed in this paper belong to the standard General Relativity Theory, the only non-standard element being their (much simpler) mathematical formulation. As a mathematical bonus, we propose a new formalism in the calculus of variations, because in case of hyperbolic field theories the standard approach leads to nonsense conclusions.

Entropy of dynamical black holes

We propose a new formula for the entropy of a dynamical black hole—valid to leading order for perturbations off of a stationary black hole background—in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in n dimensions. In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term. In particular, in general relativity, our formula for the entropy of a dynamical black hole differs from the standard Bekenstein-Hawking formula A/4 by a term involving the integral of the expansion of the null generators of the horizon. We show that, to leading perturbative order, our dynamical entropy in general relativity is equal to 1/4 of the area of the apparent horizon. Our formula for entropy in a general theory of gravity is obtained from the requirement that a “local physical process version” of the first law of black hole thermodynamics hold for perturbations of a stationary black hole. It follows immediately that for first order perturbations sourced by external matter that satisfies the null energy condition, our entropy obeys the second law of black hole thermodynamics. For vacuum perturbations, the leading-order change in entropy occurs at second order in perturbation theory, and the second law is obeyed at leading order if and only if the modified canonical energy flux is positive (as is the case in general relativity but presumably would not hold in more general theories of gravity). Our formula for the entropy of a dynamical black hole differs from a formula proposed independently by Dong and by Wall. We obtain the general relationship between their formula and ours. We then consider the generalized second law in semiclassical gravity for first order perturbations of a stationary black hole. We show that the validity of the quantum null energy condition (QNEC) on a Killing horizon is equivalent to the generalized second law using our notion of black hole entropy but using a modified notion of von Neumann entropy for matter. On the other hand, the generalized second law for the Dong-Wall entropy is equivalent to an integrated version of QNEC, using the unmodified von Neumann entropy for the entropy of matter. Published by the American Physical Society 2024

Metric perturbations in noncommutative gravity

We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.

Quantum symmetries in 2+1 dimensions: Carroll, (a)dS-Carroll, Galilei and (a)dS-Galilei

There is a surge of research devoted to the formalism and physical manifestations of non-Lorentzian kinematical symmetries, which focuses especially on the ones associated with the Galilei and Carroll relativistic limits (the speed of light taken to infinity or to zero, respectively). The investigations have also been extended to quantum deformations of the Carrollian and Galilean symmetries, in the sense of (quantum) Hopf algebras. The case of 2+1 dimensions is particularly worth to study due to both the mathematical nature of the corresponding (classical) theory of gravity, and the recently finalized classification of all quantum-deformed algebras of spacetime isometries. Consequently, the list of all quantum deformations of (anti-)de Sitter-Carroll algebra is immediately provided by its well-known isomorphism with either Poincaré or Euclidean algebra. Quantum contractions from the (anti-)de Sitter to (anti-)de Sitter-Carroll classification allow to almost completely recover the latter. One may therefore conjecture that the analogous contractions from the (anti-)de Sitter to (anti-)de Sitter-Galilei r-matrices provide (almost) all coboundary deformations of (anti-)de Sitter-Galilei algebra. This scheme is complemented by deriving (Carrollian and Galilean) quantum contractions of deformations of Poincaré algebra, leading to coboundary deformations of Carroll and Galilei algebras.

Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity

We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that any such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein’s classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.

A Postquantum Theory of Classical Gravity?

A Postquantum Theory of Classical Gravity?

Torsion in the Classical Spacetime Context

Abstract Teleparallel gravity, an empirically equivalent counterpart to general relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the torsional forces of teleparallel gravity, we consider a context in which forces are better understood: classical spacetimes. We propose a method of incorporating torsion into the classical spacetime context that yields a classical theory of gravity with a closed temporal metric and spacetime torsion. We then prove a result analogous to the Trautman degeometrization theorem: that every model of Newton–Cartan theory gives rise, non-uniquely, to a model of this theory.

Signatures of Quantum Gravity in the Gravitational Self-Interaction of Photons.

We propose relativistic tests of quantum gravity using the gravitational self-interaction of photons in a cavity. We demonstrate that this interaction results in a number of quantum gravitational signatures in the quantum state of the light that cannot be reproduced by any classical theory of gravity. We rigorously assess these effects using quantum parameter estimation theory and discuss simple measurement schemes that optimally extract their signatures. Crucially, the proposed tests are free of QED photon-photon scattering, are sensitive to the spin of the mediating gravitons, and can probe the locality of the gravitational interaction. These protocols provide a new avenue for studying the quantum nature of gravity in a relativistic setting.

Covariant formulation of refracted gravity

We propose a covariant formulation of refracted gravity (RG), which is a classical theory of gravity based on the introduction of gravitational permittivity – a monotonic function of the local mass density – in the standard Poisson equation. Gravitational permittivity mimics dark matter phenomenology. The covariant formulation of RG (CRG) that we propose belongs to the class of scalar-tensor theories, where the scalar fieldφhas a self-interaction potential 𝒱(φ) = − Ξφ, with Ξ being a normalization constant. We show that the scalar field is twice the gravitational permittivity in the weak-field limit. Far from a spherical source of densityρs(r), the transition between the Newtonian and the RG regime appears below the acceleration scaleaΞ = (2Ξ − 8πGρ/φ)1/2, withρ = ρs + ρbgandρbgbeing an isotropic and homogeneous background. In the limit 2Ξ ≫ 8πGρ/φ, we obtainaΞ ∼ 10−10m s−2. This acceleration is comparable to the accelerationa0originally introduced in MOdified Newtonian Dynamics (MOND). From CRG, we also derived the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar fieldφthat mimics dark matter also drives the accelerated expansion of the Universe. From the stress-energy tensor ofφ, we derived the equation of state of a redshift-dependent effective dark energywDE = pDE/ρDE. Current observational constraints onwDEand distance modulus data of type Ia supernovae suggest that Ξ has a comparable value to the cosmological constant Λ in the standard model. Since Ξ also plays the same role of Λ, CRG suggests a natural explanation of the known relationa0 ∼ Λ1/2. CRG thus appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, and it falls within the family of models that unify the two dark sectors, highlighting a possible deep connection between phenomena currently attributed to dark matter and dark energy separately.

Modified Gravity Approaches to the Cosmological Constant Problem

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations.

Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND

General relativity and its Newtonian weak field limit are not sufficient to explain the observed phenomenology in the Universe, from the formation of large-scale structures to the dynamics of galaxies, with the only presence of baryonic matter. The most investigated cosmological model, the ΛCDM, accounts for the majority of observations by introducing two dark components, dark energy and dark matter, which represent ∼95% of the mass-energy budget of the Universe. Nevertheless, the ΛCDM model faces important challenges on the scale of galaxies. For example, some very tight relations between the properties of dark and baryonic matters in disk galaxies, such as the baryonic Tully–Fisher relation (BTFR), the mass discrepancy–acceleration relation (MDAR), and the radial acceleration relation (RAR), which see the emergence of the acceleration scale a0≃1.2×10−10 m s−2, cannot be intuitively explained by the CDM paradigm, where cosmic structures form through a stochastic merging process. An even more outstanding coincidence is due to the fact that the acceleration scale a0, emerging from galaxy dynamics, also seems to be related to the cosmological constant Λ. Another challenge is provided by dwarf galaxies, which are darker than what is expected in their innermost regions. These pieces of evidence can be more naturally explained, or sometimes even predicted, by modified theories of gravity, that do not introduce any dark fluid. I illustrate possible solutions to these problems with the modified theory of gravity MOND, which departs from Newtonian gravity for accelerations smaller than a0, and with Refracted Gravity, a novel classical theory of gravity introduced in 2016, where the modification of the law of gravity is instead regulated by a density scale.

Nonlocal classical theory of gravity: massiveness of nonlocality and mass shielding by nonlocality

Nonlocal classical theory of gravity: massiveness of nonlocality and mass shielding by nonlocality

The Conformal Cosmological Potential

We discuss qualitative features of the conformal relation between certain classes of gravity theories and general relativity, common to different themes such as f(R), Brans-Dicke-type, and string theories. We focus primarily on the frame relations of the fields involved, slice energy, traceless and Palatini extensions, and selected cosmological applications.

On the Cosmological Transformation of Light: A Gravitational Analogue of the Photoelectric Effect

It is known that very distant galaxies, much like our own, show remarkably high receding velocities, the magnitude of which increases with distance. Therefore, in this study, a gravitational analog of the photoelectric effect was investigated by replacing the classical (wave) theory of gravity with a gravity quanta hypothesis. The significance of this concept regarding the motion of distant galaxies is evaluated by comparing the results obtained for a photon traveling through a Planck lattice model of spacetime to the observational data for both the cosmological redshift and time dilation effects of light from distant Type Ia supernovae. The photogravity effect does not necessarily invalidate the standard big bang cosmology and may in fact add a layer of fidelity to its conclusions concerning the evolution and age of the universe.

Spin‐Spacetime Censorship

AbstractQuantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, a gedanken experiment that couples the spin to spacetime is proposed, and is then analyzed in the context of quantum information by using different approaches to quantum gravity. Both classical gravity theory and certain quantum theories predict that around a spin‐half particle, the spherical symmetry of spacetime is broken by its magnetic field or merely by its intrinsic angular momentum. It is asserted that any spin‐related deviation from spherical symmetry, upon appropriate measurement, can violate relativistic causality and quantum no‐cloning. To avoid these violations, the measurable spacetime around the particle's rest frame shall typically remain spherically symmetric, potentially as a back‐action by the act of a covariant measurement, or due to a quantized spin‐dependence of the magnetic field. This way, this gedanken experiment suggests a censorship mechanism preventing the possibility of spacetime‐based spin detection, which can shed light on the interface between quantum mechanics and gravity. Since this proposed gedanken experiment is independent of any specific theory, it is suitable for testing the coupling of quantum matter and spacetime in present and future candidate theories of quantum gravity.

Bremsstrahlung of Light through Spontaneous Emission of Gravitational Waves

Zero-point fluctuations are a universal consequence of quantum theory. Vacuum fluctuations of electromagnetic field have provided crucial evidence and guidance for QED as a successful quantum field theory with a defining gauge symmetry through the Lamb shift, Casimir effect, and spontaneous emission. In an accelerated frame, the thermalisation of the zero-point electromagnetic field gives rise to the Unruh effect linked to the Hawking effect of a black hole via the equivalence principle. This principle is the basis of general covariance, the symmetry of general relativity as the classical theory of gravity. If quantum gravity exists, the quantum vacuum fluctuations of the gravitational field should also lead to the quantum decoherence and dissertation of general forms of energy and matter. Here we present a novel theoretical effect involving the spontaneous emission of soft gravitons by photons as they bend around a heavy mass and discuss its observational prospects. Our analytic and numerical investigations suggest that the gravitational bending of starlight predicted by classical general relativity should also be accompanied by the emission of gravitational waves. This in turn redshifts the light causing a loss of its energy somewhat analogous to the bremsstrahlung of electrons by a heavier charged particle. It is suggested that this new effect may be important for a combined astronomical source of intense gravity and high-frequency radiation such as X-ray binaries and that the proposed LISA mission may be potentially sensitive to the resulting sub-Hz stochastic gravitational waves.

General theory of large D membranes consistent with second law of thermodynamics

We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.

A derivation of AdS/CFT for vector models

We explicitly rewrite the path integral for the free or critical O(N) (or U(N)) bosonic vector models in d space-time dimensions as a path integral over fields (including massless high-spin fields) living on (d + 1)-dimensional anti-de Sitter space. Inspired by de Mello Koch, Jevicki, Suzuki and Yoon and earlier work, we first rewrite the vector models in terms of bi-local fields, then expand these fields in eigenmodes of the conformal group, and finally map these eigenmodes to those of fields on anti-de Sitter space. Our results provide an explicit (non-local) action for a high-spin theory on anti-de Sitter space, which is presumably equivalent in the large N limit to Vasiliev’s classical high-spin gravity theory (with some specific gauge-fixing to a fixed background), but which can be used also for loop computations. Our mapping is explicit within the 1/N expansion, but in principle can be extended also to finite N theories, where extra constraints on products of bulk fields need to be taken into account.

Unified Theory Of Gravity and Electromagnetism: Classical and Quantum Aspects

A unified classical theory of gravity and electromagnetism with a torsion vector Г_i≠ 0, proposed by S N Bose in 1952, is introduced. In this theory, the torsion vector acts as a magnetic current and it is shown that (i) the electromagnetism is invariant under continuous Heaviside–Larmor transformations and (ii) the electric and magnetic charges are topologically quantised, satisfying the Dirac quantisation condition, without implying any Dirac string provided Г_iis curl-less.