Gravitational Entropy Research Articles

The Scaling Entropy-Area Thermodynamics and the Emergence of Quantum Gravity

This article introduces the “Scaling Entropy-Area Thermodynamics” (SEAT), a unified frameworkclaiming that all gravitational systems’ entropy scales with their surface, rather their volume, allowing gravity to be explained as an emergent phenomenon. This approach reveals how entropy, information, spacetime geometry and quantum mechanics are intrinsically linked fromnotions such as von Neumann entropy, Bekenstein bound and Ryu-Takayanagi conjecture. With the help of new entropy formulations involving surface gravity, SEAT illustrates how gravitational entropy explains gravitational systems from structured information at the boundary surface. SEAT not only solves the black hole information paradox by suggesting that they evolve, as their entropy decrease, towards order, with information preserved in a progressively organized manner and emitted through the entangled Hawking radiation, but, offers by the extending of the “entropy-area” relation to all gravitational systems, to comprehend, in a unified approach, the emergent nature of gravity from how information is encoded and organized on the boundary surface.

A new class of traversable wormhole metrics

In this work, we have formulated a new class of traversable wormhole metrics. Initially, we have considered a wormhole metric in which the temporal component is an exponential function of r but the spatial components of the metrics are fixed. Following that, we have again constructed a generalized wormhole metric in which the spatial component is an exponential function of r, but the temporal component is fixed. Finally, we have considered the generalized wormhole metric in which both the temporal and spatial components are generalized exponential functions of r. We have also studied some of their properties including throat radius, stability, and energy conditions, examined singularity, the metric in curvature coordinates, effective refractive index, innermost stable circular orbit (ISCO) and photon sphere, Regge–Wheeler potential and their quasinormal modes, gravitational entropy, and determined the curvature tensor. The radius of the throat is found to be consistent with the properties of wormholes and does not contain any types of singularities. Most interestingly, we find that their throat radius is the same for the same spatial component and the same range of values of m. In addition to these, they also violate the Null Energy Condition (NEC) near the throat. These newly constructed metrics form a new class of traversable wormholes.

Evolution of creases on the event horizon of a black hole merger

A generic black hole merger occurs through a restructuring of creases (sharp edges) on the event horizon. This process is studied for a black hole merger in the limit of infinite mass ratio, for which constructing the event horizon reduces to finding a null hypersurface that asymptotes to a Rindler horizon in the Kerr spacetime. Geometrical properties of the creases on this horizon are determined and the results are compared with the predictions of an exact local description of the event horizon in a generic merger. The crease set is shown to have finite area. A recently proposed expression for the gravitational entropy of a crease is shown to diverge at the instant of merger. Caustics on (and off) the event horizon are determined by exploiting the correspondence with the problem of gravitational lensing by a Kerr black hole. Caustics form an “astroid tube” in spacetime, two edges of which lie on the event horizon of the merger. Perturbative expressions for the location of this tube are presented, extending previous work to much higher perturbative order. Published by the American Physical Society 2024

Cornering gravitational entropy

We present a new derivation of gravitational entropy functionals in higher-curvature theories of gravity using corner terms that are needed to ensure well-posedness of the variational principle in the presence of corners. This is accomplished by cutting open a manifold with a conical singularity into a wedge with boundaries intersecting at a corner. Notably, our observation provides a rigorous definition of the action of a conical singularity that does not require regularization. For Einstein gravity, we compute the Rényi entropy of gravitational states with either fixed-periodicity or fixed-area boundary conditions. The entropy functional for fixed-area states is equal to the corner term, whose extremization follows from the variation of the Einstein action of the wedge under transverse diffeomorphisms. For general Lovelock gravity the entropy functional of fixed-periodicity states is equal to the Jacobson-Myers (JM) functional, while fixed-area states generalize to fixed-JM-functional states, having a flat spectrum. Extremization of the JM functional is shown to coincide with the variation of the Lovelock action of the wedge. For arbitrary F(Riemann) gravity, under special periodic boundary conditions, we recover the Dong-Lewkowycz entropy for fixed-periodicity states. Since the variational problem in the presence of corners is not well-posed, we conjecture the generalization of fixed-area states does not exist for such theories without additional boundary conditions. Thus, our work suggests the existence of entropy functionals is tied to the existence of corner terms which make the Dirichlet variational problem well-posed.

Generalized covariant entropy bound in Einstein gravity with quadratic curvature corrections

We explore the generalized covariant entropy bound in the theory where Einstein gravity is perturbed by quadratic curvature terms, which can be viewed as the first-order quantum correction to Einstein gravity. By replacing the Bekenstein-Hawking entropy with the holographic entanglement entropy of this theory and introducing two reasonable physical assumptions, we demonstrate that the corresponding Generalized Covariant Entropy Bound is satisfied under a first-order approximation of the perturbation from the quadratic curvature terms. Our findings suggest that the entropy bound and the Generalized Second Law of black holes are satisfied in the Einstein gravity under the first-order perturbation from the quadratic curvature corrections, and they also imply that the generalized covariant entropy bound may still hold even after considering the quantum correction of gravity, but in this case, we may need to use holographic entanglement entropy as the formula for gravitational entropy.

Arrow of time and gravitational entropy in collapse

We investigate the status of the gravitational arrow of time in the case of a spherical collapse of a fluid that conducts heat and radiates energy. In particular, we examine the results obtained by W. B. Bonnor in his 1985 paper where he found that the gravitational arrow of time was opposite to the thermodynamic arrow of time. The measure of gravitational epoch function P used by Bonnor was given by the ratio of the Weyl square to the Ricci square. In this paper, we have assumed the measure of gravitational entropy (GE) P 1 to be given by the ratio of the Weyl scalar to the Kretschmann scalar. Our analysis indicates that Bonnor’s result seems to be validated, i.e. the gravitational arrow and the thermodynamic arrow of time point in opposite directions. This strengthens the opinion that the Weyl proposal of GE applies only to the Universe as a whole (provided that we exclude the white holes).

A compendium of logarithmic corrections in AdS/CFT

We study the logarithmic corrections to various CFT partition functions in the context of the AdS4/CFT3 correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordström black holes in AdS4. Our results also have important implications for effective field theory coupled to gravity in AdS4 and for the existence of scale-separated AdS4 vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields.

Gravitational entropy and the flatness, homogeneity and isotropy puzzles

We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are Einstein's theory of gravity and Hawking's method of computing the gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for “big bang” type singularities dominated by conformal matter, enforcing CPT symmetry and analyticity. Besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons from which we calculate the total gravitational entropy Sg of cosmologies including radiation, dark energy and space curvature of either sign. We find Sg∼SΛ1/4Sr, where SΛ is the de Sitter entropy and Sr is the total entropy in radiation, which is extensive in the comoving spatial volume. Thus, Sg can be larger than SΛ and we show it is largest for universes which are spatially flat. Extending our analysis to include linearized perturbations, we show that, for a given set of globally conserved quantities, Sg is greatest for universes that are also homogeneous and isotropic on large scales.

Thermodynamic solution of the homogeneity, isotropy and flatness puzzles (and a clue to the cosmological constant)

We obtain the analytic solution of the Friedmann equation for fully realistic cosmologies including radiation, non-relativistic matter, a cosmological constant λ and arbitrary spatial curvature κ. The general solution for the scale factor a(τ), with τ the conformal time, is an elliptic function, meromorphic and doubly periodic in the complex τ-plane, with one period along the real τ-axis, and the other along the imaginary τ-axis. The periodicity in imaginary time allows us to compute the Hawking temperature and the global gravitational entropy of cosmological spacetimes, just as Gibbons, Hawking and Perry did for black holes and de Sitter spacetime. The global gravitational entropy favours universes like our own which are spatially flat, homogeneous, and isotropic, with a small positive cosmological constant.

Quantum Entropy and the Mechanism of Gravity

Quantum entropy measures the number of possible microstates of position and momentum due to quantum uncertainty. Black hole entropy is an example of quantum entropy. Classical entropy, like the Gibbs entropy of a gas, does not depend on quantum uncertainty. This paper is the first to define the quantum entropy of ordinary matter, termed “atomic entropy”. The atomic entropy at the surface of a spherical object depends on its mass and is inversely proportional to its surface area. The entropy scale factor (ESF) is a theory that all changes in the scale of spacetime are due to differences in entropy. Defining atomic entropy allows the ESF to make predictions for systems including ordinary matter. In the ESF, gravitational objects are attracted to one another because gravitational entropy, a form of quantum entropy, increases as the distance between these objects decreases. The increase in gravitational entropy increases the total entropy of the system, in accordance with the second law of thermodynamics. This paper is also the first to use the gradients in the scale of space and time predicted by the ESF to derive Newtonian gravity. Explaining the mechanism of gravity in this way provides a link between quantum physics and gravity.

New gravastar model in generalised cylindrically symmetric space–time and prediction of mass limit

We present a class of new Gravastar solutions following the works of Mazur and Mottola for a Gravitational Bose–Einstein Condensate (GBEC) star in generalised cylindrically symmetric space–time. A stable gravastar consists of 3 distinct regions, namely: (i) an interior de-Sitter space (p=−ρ), which exerts an outwards repulsive force at all points on the thin shell, (ii) an intermediate thin shell with a slice of finite length separating the interior and exterior regions is supposed to be consisting of an ultra-relativistic stiff fluid, with the equation of state p=ρ and (iii) an exterior vacuum region. This thin shell, which is considered as the critical surface for the quantum phase transition, replaces both the classical de-Sitter space and Schwarzschild event horizon. The new solutions are free from any singularities. The energy density, total energy, proper length, and the entropy of this shell are explored in this model. From the thin shell solution and using Lanczos equations for stress energy density, we have predicted the mass contained into the gravastar shell. The stability of the gravastar model is analysed through the consideration of gravitational surface redshift and entropy calculation. We have also obtained a constraint on the possible mass of the thin shell without violating the condition for stable gravastar configuration. All these features indicate that the present model is physically viable.

Gravitational entropy of stringy charged black holes in teleparallel gravity

In order to resolve several theoretical and practical flaws in general relativity GR, a variety of modified theories of gravity have been proposed. One exciting strategy is to modify gravity’s geometrical nature. The teleparallel theory of gravity accomplishes this. In this paper, we study the gravitational energy GE and gravitational pressure of stringy charged black holes SCBH namely within the basic framework of the teleparallel equivalent of general relativity GR. We determine GE bounded by the event horizon of the black hole BH and the radial pressure RP over it. Furthermore, we examine the gravitational entropy of SCBH which is affected by BH’s mass m and charge Q.

Entropy of the entangled Hawking radiation

Entropic information theory, as a unified informational theory, presents a new informational theoretical framework capable of fully describing the evaporation of the black holes phenomenon while resolving the information paradox, reconciling quantum formalism and relativistic formalism in a single approach. With a set of five new equivalent equations expressing entropy, and by introducing the Hawking temperature into one of them, it is possible to solve the black holes information paradox by being able to calculate the entropy of entangled Hawking radiation, entangled with the fields inside black holes, allowing us to extract information from inside black holes. The proposed model solves the information paradox of black holes by calculating a new entropy formula for the entropy of black holes as equal to the entropy of the pure state of entangled Hawking radiation, itself equal to the fine-grained entropy or von Neumann entropy, itself according to the work of Casini and Bousso equal to the Bekenstein bound which is itself equal, being saturated by Bekenstein-Hawking entropy, at this same entropy. Moreover, since the law of the entropy horizon of black holes turns out to be a special case of the Ryu-Takayanagi conjecture, this general formula for the fine-grained entropy of quantum systems coupled to gravity, equalizes the entropy of entangled Hawking radiation with the gravitational fine-grained entropy of black holes, and makes it possible to relate this resolution of the information paradox of black holes based on the concept of mass of the information bit to quantum gravity explaining the emergence of the quantum gravity process through the fundamentality of entangled quantum information.

A proposal for 3d quantum gravity and its bulk factorization

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a q-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of PSL(2, ℝ) ⨂ PSL(2, ℝ). We show that the correct calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group {textrm{SL}}_q^{+}left(2,mathbb{R}right)bigotimes {textrm{SL}}_q^{+}left(2,mathbb{R}right) . Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.

Vacuum energy density and gravitational entropy

The failure to calculate the vacuum energy is a central problem in theoretical physics. Presumably the problem arises from the insistent use of effective field theory reasoning in a context that is well beyond its intended scope. If one follows this path, then one is led inevitably to statistical or anthropic reasoning for observations. It appears that a more palatable resolution of the vacuum energy problem requires some form of UV/IR feedback. In this paper we take the point of view that such feedback can be thought of as arising by defining a notion of quantum space-time. We reformulate the regularized computation of vacuum energy in such a way that it can be interpreted in terms of a sum over elementary phase space volumes, that we identify with a ground state degeneracy. This observation yields a precise notion of UV/IR feedback, while leaving a scale unfixed. Here we argue that holography can be thought to provide a key piece of information: we show that equating this microscopic ground state degeneracy with macroscopic gravitational entropy yields a prediction for the vacuum energy that can easily be consistent with observations. Essentially, the smallness of the vacuum energy is tied to the large size of the Universe. We discuss how within this scenario notions of effective field theory can go so wrong.

The Emergent Entangled Informational Universe

The dream of capturing the workings of the entire universe in a single equation or a simple set of equations is still pursued. A set of five new equivalent formulations of entropy based on the introduction of the mass of the information bit in Louis de Broglie's hidden thermodynamics and on the physicality of information, is proposed, within the framework of the emergent entangled informational universe model, which is based on the principle of strong emergence, the mass-energy-information equivalence principle and the Landauer’s principle. This model can explain various process as informational quantum processes such energy, dark matter, dark energy, cosmological constant and vacuum energy. The dark energy is explained as a collective potential of all particles with their individual zero-point energy emerging from an informational field, distinct from the usual fields of matter of quantum field theory, associated with dark matter as having a finite and quantifiable mass; while resolving the black hole information paradox by calculating the entropy of the entangled Hawking radiation, and shedding light on gravitational fine-grained entropy of black holes. This model explains the collapse of the wave function by the fact that a measure informs the measurer about the system to be measured and, this model is able to invalidate the many worlds interpretation of quantum mechanics and the simulation hypothesis.

Emergent area laws from entangled matrices

We consider a wavefunction of large N matrices supported close to an emergent classical fuzzy sphere geometry. The SU(N) Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric subregion and their complement. We call this ‘Gauss law entanglement’. We show that the subregion degrees of freedom transform under a single dominant, low rank representation of SU(N). The corresponding Gauss law entanglement entropy is given by the logarithm of the dimension of this dominant representation. It is found that, after coarse-graining in momentum space, the SU(N) Gauss law entanglement entropy is proportional to the geometric area bounding the subregion. The constant of proportionality goes like the inverse of an emergent Maxwell coupling constant, reminiscent of gravitational entropy.

Gravitational entropy of Hayward black hole

We analyze the gravitational entropy defined by the Weyl curvature for the Hayward black hole, which is one of the regular black holes without singularity in the event horizon. Using the definition by the ratio of the Weyl curvature scalar and the Kretschmann scalar as the entropy measure, we evaluate the gravitational entropy on the outer and inner horizons. We derive an expression for the curvature tensor of the Hayward black hole that is as independent as possible of the parameter added to the black hole and give an equation for the entropy measure explicitly independent of that parameter. The gravitational entropy density used in previous studies presents questions from the standpoint of mathematical rigor while we discuss possible improvements in its definition. We compare the results for the Hayward black hole with the analysis for the Reisner–Nordstöm black hole and discuss the effect of singularity resolution on gravitational entropy.

Entropic gravity and cosmology in Kaniadakis statistics

By using the Kaniadakis statistics, we discuss the modifications of Newtonian gravity and radial velocity profile in the light of Verlinde’s formalism for gravitational entropy. After considering the implications of [Formula: see text]-statistics on the gravitational potential, it is shown that an accelerated universe may be obtained by considering the Friedmann first equation in this nonextensive statistics.

Microstates of position and momentum result in gravitational entropy

Measurements of a black hole’s position are limited in four different ways: Absorption of short-wavelength photons by the black hole, gravitational lensing’s interference with geometric diffraction, gravitational redshift decreasing the resolution of interactions close to the event horizon, and the relatively long wavelength of Hawking radiation. These limitations mean that a black hole cannot be localized more precisely than its Schwarzschild radius. Limitations on measuring mass and velocity mean that the position and momentum of a black hole cannot be simultaneously known more precisely than 2 h rs/lP , a value more restrictive than the Heisenberg uncertainty principle. Hidden information about a black hole’s position and momentum results in many possible microstates that are indistinguishable to an observer. One way to interpret the physical meaning of Bekenstein‐Hawking entropy is as a measure of the number of these microstates. This interpretation allows entropy to be generalized to objects in any gravitational field, because gravitational redshift increases uncertainty about position and momentum for objects in all gravitational fields, not just those of black holes.