Hole Entropy Research Articles

Scrambling time for analogue black holes embedded in AdS space

We propose a gedanken experiment on realizing thermofield double state (TFD) by using analog black holes and provide an approach to test the scrambling time. Through this approach, we demonstrate clearly how shock wave changes the TFD state as time evolves. As the whole system evolves forward in time, the perturbation of space-time geometry will increase exponentially. Finally, it will destroy the entanglement between the two states of the thermal field, and the mutual information between them is reduced to zero in the time scale of scrambling. The results show that for perturbations of analogue black holes embedded in AdS space, the scale of the scrambling time is closely related to the logarithm of entropy of the black hole. The results provide further theoretical argument for the scrambling time, which can be further falsified in experiments.

Quantum extremal islands made easy. Part IV. Massive black holes on the brane

We study two-dimensional eternal black holes with non-zero mass, where each asymptotic boundary is in contact with a CFT on a circle, following the doubly holographic braneworld models constructed in [1–3]. We compute the Page curve of the black hole (or the bath CFTs), which amounts to finding different geodesics in the bulk BTZ geometry with a Randall-Sundrum brane falling into the black hole. We also explore the possibility of including an intrinsic JT gravity action on the brane. As expected, the generalized entropy rises linearly at early times. However, there is a transition to a late-time phase in which the entropy remains constant. The value of the late-time entropy depends on the size of the thermal baths. For a small size, it corresponds to the thermal entropy of the baths, while for large size, it corresponds to twice the horizon entropy of the black hole. The critical size and the Page time are proportional to ratio of the central charges of the conformal defect and the bath CFT.

Unitarity and Page Curve for Evaporation of 2D AdS Black Holes.

We explore the Hawking evaporation of two-dimensional anti-de Sitter (AdS), dilatonic black hole coupled with conformal matter, and derive the Page curve for the entanglement entropy of radiation. We first work in a semiclassical approximation with backreaction. We show that the end-point of the evaporation process is AdS with a vanishing dilaton, i.e., a regular, singularity-free, zero-entropy state. We explicitly compute the entanglement entropies of the black hole and the radiation as functions of the horizon radius, using the conformal field theory (CFT) dual to AdS gravity. We use a simplified toy model, in which evaporation is described by the forming and growing of a negative mass configuration in the positive-mass black hole interior. This is similar to the “islands” proposal, recently put forward to explain the Page curve for evaporating black holes. The resulting Page curve for AdS black holes is in agreement with unitary evolution. The entanglement entropy of the radiation initially grows, closely following a thermal behavior, reaches a maximum at half-way of the evaporation process, and then goes down to zero, following the Bekenstein–Hawking entropy of the black hole. Consistency of our simplified model requires a non-trivial identification of the central charge of the CFT describing AdS gravity with the number of species of fields describing Hawking radiation.

Thermodynamic corrections of Gauss–Bonnet black hole under general uncertainty principle

In this paper, the thermodynamics of Gauss–Bonnet black hole is investigated. We calculate the analytical solutions of corresponding thermodynamic variables, e.g. the Hawking temperature, entropy of the black hole at its event horizon. In addition, we derive the heat capacity to analyze the thermal stability of the black hole. We also compute the rate of emission in terms of photons through tunneling. By adopting a numerical method to analyze their properties, an obvious phase transition behavior is found. Furthermore, according to the general uncertainty principle, we study the quantum corrections to these thermodynamic quantities and obtain the quantum-corrected entropy containing the logarithmic term. At last, we investigate the effects of the Gauss–Bonnet coupling parameter [Formula: see text] and generalized uncertainty principle parameter [Formula: see text] on the thermodynamics of Gauss–Bonnet black hole.

Lung Cancer Detection and Severity Level Classification Using Sine Cosine Sail Fish Optimization Based Generative Adversarial Network with CT Images

Abstract This paper develops a lung nodule detection mechanism using the proposed sine cosine Sail Fish (SCSF) based generative adversarial network (GAN). However, the proposed SCSF-based GAN is designed by integrating the sine cosine algorithm with the SailFish optimizer, respectively. By using pre-processing, lung nodule segmentation, feature extraction, lung cancer detection, and severity level classification methods detection and classification are performed. The pre-processed computed tomography (CT) image is fed to the lung nodule segmentation phase, where the CT image is segmented into different sub-images to exactly detect the abnormal region. The segmented result after segmentation is fed to the feature extraction phase, where the features like mean, variance, entropy and hole entropy, are extracted from the nodule region. The affected regions are accurately detected using the loss function of the discriminator component. Finally, the lung nodules are detected and classified using the proposed SCSF-based GAN. The proposed approach obtained better performance with the accuracy of 96.925%, sensitivity of 96.900% and specificity of 97.920% for the first-level classification, and the accuracy of 94.987%, the sensitivity of 94.962% and specificity of 95.962% for second-level classification, respectively.

Black hole entropy sourced by string winding condensate

We calculate the entropy of an asymptotically Schwarzschild black hole, using an effective field theory of winding modes in type II string theory. In Euclidean signature, the geometry of the black hole contains a thermal cycle which shrinks towards the horizon. The light excitations thus include, in addition to the metric and the dilaton, also the winding modes around this cycle. The winding modes condense in the near-horizon region and source the geometry of the thermal cycle. Using the effective field theory action and standard thermodynamic relations, we show that the entropy, which is also sourced by the winding modes condensate, is exactly equal to the Bekenstein-Hawking entropy of the black hole. We then discuss some properties of the winding mode condensate and end with an application of our method to an asymptotically linear-dilaton black hole.

Black hole thermodynamics in the presence of a maximal length and minimum measurable in momentum

In this work, incorporating the effect of the minimum measurable in momentum and maximal length, we studied the thermodynamics property of the Schwarzschild black hole and the Unruh effect. According to this scenario, we see that the black hole temperature cannot be smaller than a certain minimum value . Moreover, we find that black hole mass cannot be larger than a maximum mass value . Considering these findings first we compute the corrected Hawking temperature vs. the mass and examine its characteristic behavior. Then, we derive the black hole's entropy and heat capacity. We find that the black hole is stable when . Finally, we examined the modified Unruh effect. We find that the modified Unruh temperature explicitly depends on α.

Quantum gravity corrections to tunneling of spin-1/2 fermions from Kerr–Newman Black Hole

In this paper, we solve the Dirac Equation in curved space–time, modified by the generalized uncertainty principle, in the presence of an electromagnetic field. Using this, we study the tunneling of [Formula: see text]-spin fermions from Kerr–Newman black hole. Corrections to the Hawking temperature and entropy of the black hole due to quantum gravity effects are also discussed.

On Hawking entropy revisited

The teleparallel gravity, in the weak field approximation, is considered. In the Schwarzschild space–time the gravitational Stefan–Boltzmann law is calculated. Using the first law of thermodynamics, the Hawking entropy and temperature of the black hole are calculated. Thermofield dynamics formalism is used to define the temperature-dependent theory. In addition the gravitational Casimir effect and Stefan–Boltzmann law at zero and finite temperature are calculated in Schwarzschild space–time.

A Contextual Planck Parameter and the Classical Limit in Quantum Cosmology

We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, l_{P}, but for those larger than l_{Q}=(l_{P}^{2}H^{-1})^{1/3}, where H is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole.

Thermodynamics and weak cosmic censorship conjecture of 4D Gauss-Bonnet-Maxwell black holes via charged particle absorption * *Supported in part by the NSFC (11875196, 11375121, 11005016, 11947225)

Recently, the non-trivial solutions for 4-dimensional black holes of Einstein-Gauss-Bonnet gravity had been discovered. In this paper, considering a charged particle entering into a 4-dimensional Gauss-Bonnet-Maxwell black hole, we calculate the black hole thermodynamic properties using the Hamilton-Jacobi equation. In the normal phase space, the cosmological constant and Gauss-Bonnet parameter are fixed, the black hole satisfies the first and second laws of thermodynamics, and the weak cosmic censorship conjecture (WCCC) is valid. On the other hand, in the case of extended phase space, the cosmological constant and Gauss-Bonnet parameter are treated as thermodynamic variables. The black hole also satisfies the first law of thermodynamics. However, the increase or decrease in the black hole's entropy depends on some specific conditions. Finally, we observe that the WCCC is violated for the near-extremal black holes in the extended phase space.

Static topological black hole with a nonminimal derivative coupling and a nonlinear electromagnetic field of Born-Infeld type

We consider scalar-tensor gravity with nonminimal derivative coupling and Born-Infeld electromagnetic field which is minimally coupled to gravity. Since cosmological constant is taken into account it allowed us not only derive static black hole with spherical horizon but also to obtain topological solutions with non-spherical horizons. The obtained metrics are thoroughly analyzed, namely for different distances and types of topology of horizon. To investigate singularities of the metrics Kretschmann scalar is used and it is shown that the character of singularity depends on the type of topology of horizon and dimension of space. We also investigate black hole's thermodynamics, namely we obtain and examine black hole's temperature. To derive the first law of black hole's thermodynamics Wald's approach is applied. Nonetheless this approach is well established, there is ambiguity in definition of black hole's entropy which can be resolved just by virtue of some independent approach.

Systolic Aspects of Black Hole Entropy

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections Σ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of Σ are violated in quantum theory. We choose the systoles of Σ to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of Σ . We focus on the limiting case of Σ having a large genus.

On a Possibly Pure Set-Theoretic Contribution to Black Hole Entropy

Continuity as appears to us immediately by intuition (in the flow of time and in motion) differs from its current formalization, the arithmetical continuum or equivalently the set of real numbers used in modern mathematical analysis. Motivated by the known mathematical and physical problems arising from this formalization of the continuum, our aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness of the arithmetical continuum, a formal set-theoretic entropy is assigned to the arithmetical continuum. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the arithmetical continuum in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too.

Generalized Klein\u2013Gordon equation and quantum gravity corrections to tunneling of scalar particles from Kerr\u2013Newman black hole

In this article we deduce the generalized Klein–Gordon Equation in curved spacetime in the presence of an electromagnetic field from first principles, using the generalized uncertainty principle. Using this equation we study the tunneling of scalar particles from a Kerr–Newman black hole. Corrections to the Hawking temperature and entropy of the black hole due to quantum gravity effects are discussed.

Hyperbolic fracton model, subsystem symmetry, and holography

We propose that the fracton models with subsystem symmetry can be a class of toy models for the holographic principle. The discovery of the anti-de Sitter/conformal field theory correspondence as a concrete construction of holography and the subsequent developments including the subregion duality and Ryu-Takayanagi formula of entanglement entropy have revolutionized our understanding of quantum gravity and provided powerful tool sets for solving various strongly-coupled quantum field theory problems. To resolve many mysteries of holography, toy models can be very helpful. One example is the holographic tensor networks which illuminate the quantum error correcting properties of gravity in the anti-de Sitter space. In this work we discuss a classical toy model featuring subsystem symmetries and immobile fracton excitations. We show that such a model defined on the hyperbolic lattice satisfies some key properties of the holographic correspondence. The correct subregion duality and Ryu-Takayanagi formula for mutual information are established for a connected boundary region. A naively defined black hole's entropy scales as its horizon area. We also present discussions on corrections for more complicated boundary subregions, the possible generalizations of the model, and a comparison with the holographic tensor networks.

Warped AdS3 black hole in minimal massive gravity with first order formalism

We obtain a black hole solution of minimal massive gravity theory with Maxwell and electromagnetic Chern-Simons terms using the first order formalism. This black hole solution can be translated into the spacelike warped $AdS_3$ black hole solution with some parameters' conditions changing their coordinates system into a Schwarzschild one. Applying the Wald formalism to this theory with the first order formalism, we also find out the entropy, mass, and angular momentum of this black hole solution satisfies the first law of black hole thermodynamics. Under the assumption that minimal massive gravity theory with suitable asymptotically warped $AdS_3$ boundary conditions is holographically dual to a two dimensional boundary conformal field theory, we find appropriate central charges by using the relations between entropy of this black hole and the Cardy formula in dual conformal field theory described by left and right moving central charges and temperatures.

Bulk view of teleportation and traversable wormholes

We construct detailed AdS2 gravity solutions describing the teleportation through a traversable wormhole sending a state from one side of the wormhole to the other. The traversable wormhole is realized by turning on a double trace interaction that couples the two boundaries of an eternal AdS2 black hole. The horizon radius or the entropy of the black hole is reduced consistently with the boundary computation of the energy change, confirming the black hole first law. To describe teleportee states traveling through the wormhole, we construct Janus deformations which make the Hamiltonians of left-right boundaries differ from each other by turning on exact marginal operators. Combining explicitly the traversable wormhole solution and the teleportee states, we present a complete bulk picture of the teleportation in the context of ER=EPR. The traversability of the wormhole is not lost to the leading order of the deformation parameter. We also consider solutions where the teleportee meets the matter thrown from the other side during teleportation, in accordance with the assertion that the bulk wormhole is experimentally observable.

Decreasing entropy of dynamical black holes in critical gravity

Critical gravity is a quadratic curvature gravity in four dimensions which is ghost-free around the AdS background. Constructing a Vaidya-type exact solution, we show that the area of a black hole defined by a future outer trapping horizon can shrink by injecting a charged null fluid with positive energy density, so that a black hole is no more a one-way membrane even under the null energy condition. In addition, the solution shows that the Wald-Kodama dynamical entropy of a black hole is negative and can decrease. These properties expose the pathological aspects of critical gravity at the non-perturbative level.

On the on-shell: the action of AdS4 black holes

We compute the on-shell action of static, BPS black holes in AdS4 from mathcal{N}=2 gauged supergravity coupled to vector multiplets and show that for a certain class it is equal to minus the entropy of the black hole. Holographic renormalization is used to demonstrate that with Neumann boundary conditions on the scalar fields, the divergent and finite contributions from the asymptotic boundary vanish. The entropy arises from the extrinsic curvature on Σg × S1 evaluated at the horizon, where Σg may have any genus g ≥ 0. This provides a clarification of the equivalence between the partition function of the twisted ABJM theory on Σg × S1 and the entropy of the dual black hole solutions. It also demonstrates that the complete entropy resides on the AdS2 × Σg horizon geometry, implying the absence of hair for these gravity solutions.