It is well-known that in order to make the action well defined, one may employ different kinds of boundary conditions (BCs) accompanied by the appropriate Gibbons-Hawking-York (GHY) terms. In this paper we investigate the role of the selected BC and the corresponding GHY terms on the black hole (BH) entropy. Our result shows, regardless of the kind of BC, the BH entropy in all cases is the same as one obtained under Dirichlet BC from Wald formula or semi-classical approximation method. We considered the Schwarzschild solution for $f(R)$-gravity and general relativity (GR) in standard dimensions as special models.
We review the renormalization of one-loop effective action for gravity coupled to a scalar field and that of the Bekenstein-Hawking entropy of a black hole plus the statistical entropy of the scalar field. It is found that the total entropy of the black hole's geometric entropy and the statistical entropy yields the renormalized Bekenstein-Hawking area-law of black hole entropy only for even dimensional Reissner-Nördstrom (Schwarzschild) black holes. We discuss the problem of the microscopic origin of black hole entropy in connection with the renormalization of black hole entropy.
Black hole entropy is shown to be a consequence of restricting our description of physics to the exterior of black holes. This precludes the need for a statistical mechanical description of this entropy in terms of microstates.
The Hod conjecture proposes that the asymptotic quasinormal frequencies determine the entropy quantum of a black hole. Considering the Maggiore modification of this conjecture we calculate the entropy spectra of general, single horizon, asymptotically flat black holes in two-dimensional dilaton gravity. We also compute the entropy quanta of the two-dimensional Witten and AdS(2) black holes. Using the results for the entropy quanta of these two-dimensional black holes we discuss whether the produced values are generic. Finally we extend the results on the entropy spectra of other black holes.
The objectivity of black hole entropy is discussed in the particular case of a Schwarzchild black hole. Using Jaynes' maximum entropy formalism and Euclidean path integral evaluation of partition function, it is argued that in the semiclassical limit when the fluctutation of metric is neglected, the black hole entropy of a Schwarzchild black hole is equal to the maximal information entropy of an observer whose sole knowledge of the black hole is its mass. Black hole entropy becomes a measure of number of its internal mass eigenstates in accordance with the Boltzmann principle only in the limit…
We calculate the entropy of spherically symmetric regular black holes by the path integral and Noether-charge method. Both methods provide an evidence that the entropy of regular black holes should be proportional to quarter of area, and there is no violation of entropy/area law at all.
We study the entropy spectrum of (2+1) BTZ black holes in massive gravity models. We use the formalism proposed by Jiang and Han where black hole property of adiabaticity and the oscillating velocity of the black hole horizon are used to investigate the quantization of the entropy of such systems. We find that the entropy of the BTZ black holes in massive gravity is quantized with equally spaced spectra.
In this paper we derive a class of rotating embedded black holes. Then we study Hawking's radiation effects on these embedded black holes. The surface gravity, entropy and angular velocity are given for each of these black holes.
Using the AdS/CFT correspondence we calculate the explicit form of the entanglement entropy for the charged BTZ black hole. The leading term in the large temperature expansion of the entropy function for this black hole reproduces its Bekenstein-Hawking entropy and the subleading term, representing the first corrections due to quantum entanglement, behaves as a logarithm of the BH entropy.
Vast amounts of entropy are produced in black hole formation, and the amount of entropy stored in supermassive black holes at the centers of galaxies is now much greater than the entropy free in the rest of the universe. Either mergers involved in forming supermassive black holes are rare,or the holes must be very efficient at capturing nearly all the entropy generated in the process. We argue that this information can be used to constrain supermassive black hole production, and may eventually provide a check on numerical results for mergers involving black holes.
Based on a recent proposal for the volume inside a black hole, we calculate the entropy associated with this volume and show that such entropy is proportional to the surface area of the black hole. Together with the consideration of black hole radiation, we find that the thermodynamics associated with the entropy is likely to be caused by the vacuum polarization near the horizon.
The classical first law of thermodynamic for Kerr-Newmann black hole (KNBH) is generalized to that in quantum form on event horizon. Then four quantum conservation laws on the KNBH equilibrium radiation process are derived, and Bekenstein-Hawking's relation S=A/4 is recovered. It can be argued that the classical entropy of black hole arise from the quantum entropy of field quanta or quasi-particles inside the hole.
Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How does the departure from pure thermal spectrum affect the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained from tunnel effect. Using the partition function, we compute the black hole entropy and derive the expression of the black hole entropy after considering the radiation. And we derive the entropy of charged black hole. In …
Adopting thin film brick-wall model, we calculate the entropy of a nonuniformly rectilinearly accelerating non-stationary black hole expressed by Kinnersley metric. Because the black hole is accelerated, the event horizon is axisymmetric. The different points of horizon surface may have different temperature. We calculate the temperature and the entropy density at every point of the horizon at first, then we obtain the total entropy through integration, which is proportional to the aera of event horizon as the same as the stationary black holes. It is shown that the black hole entropy may be r…
In this paper, we calculated the entropy of the BTZ black hole in the framework of loop quantum gravity. We got the result that the horizon degrees of freedom can be described by the 2D SO(1,1) punctured BF theory. Finally we got the area law for the entropy of BTZ black hole.
We derive a class of non-stationary embedded rotating black holes and study the Hawking's radiation effects on these embedded black holes. The surface gravity, entropy and angular velocity, which are three important properties of black holes, are presented for each of these embedded black holes.
There are exact solutions to Einstein's equations with negative cosmological constant that represent black holes whose event horizons are manifolds of negative curvature, the so-called topological black holes. Among these solutions there is one, the massless topological black hole, whose mass is equal to zero. Hod proposes that in the semiclassical limit the asymptotic quasinormal frequencies determine the entropy spectrum of the black holes. Taking into account this proposal, we calculate the entropy spectrum of the massless topological black hole and we compare with the results on the entrop…
The entropy increases enormously when a star collapses into a black hole. This entropy increase is interpreted as the decrease of the temperature due to the increase of the volume. Through these investigation the microscopic states of the black hole entropy is naturally understood as the statistical states of the enlarged phase space.
Taking the horizon surface of the black hole as a compact membrane and solving the oscillation equation of this membrane by Klein-Gordon equation, we derive the frequencies of oscillation modes of the horizon surface, which are proportional to the radiation temperature of the black hole. However, the frequencies of oscillation modes are not equidistant. Using the distribution of obtained frequencies of oscillation mode we compute the statistic entropy of the black hole and obtain that the statistic entropy of the black hole is proportional to the area of the horizon. Therefore, it is proven th…
Simple arguments related to the entropy of black holes strongly constrain the spectrum of the area operator for a Schwarzschild black hole in loop quantum gravity. In particular, this spectrum is fixed completely by the assumption that the black hole entropy is maximum. Within the approach discussed, one arrives in loop quantum gravity at a quantization rule with integer quantum numbers $n$ for the entropy and area of a black hole.
The definition of entropy obtained for stationary black holes is extended in this paper to the case of non-stationary black holes. Entropy is defined as a macroscopical thermodynamical quantity which satisfies the first principle of thermodynamics. In the non-stationary case a volume term appears since the solution does not admit a Killing vector.
Using a simple analysis based on the measurement procedure for a quantized area we explain the 1/4 factor in the Bekenstein-Hawking black hole formula A/4 for the entropy.
We consider Unruh effect as an origin for Schwarzschild black hole entropy thus implying unitarian evolution of gravity. We simulate the black hole by set of Unruh horizons and estimate total entropy of the system. Dependence on mass and spin of the emitted particles is taken into account. The obtained results may be easily extended to any other intrinsic degrees of freedom of the particles. Unruh effect contribution to Schwarzschild black hole entropy is presented in exact analytical form.
We elaborate the renormalization process of entropy of a nonextremal and an extremal Reissner-Nordström black hole by using the Pauli-Villars regularization method, in which the regulator fields obey either the Bose-Einstein or Fermi-Dirac distribution depending on their spin-statistics. The black hole entropy involves only two renormalization constants. We also discuss the entropy and temperature of the extremal black hole.
We study the entropy of black holes in the deformed Horava-Lifshitz gravity with coupling constant lambda. For lambda=1, the black hole resembles the Reissner-Norstrom black hole with a geometric parameter acting like the electric charge. Therefore, we obtain some differences in the entropy when comparing with the Schwarzschild black hole. Finally, we study the heat capacity and the thermodynamical stability of this solution.
The notion of black-hole entropy was introduced by Jacob Bekenstein in 1972. During past 45 years this subject was in the center of interests of the modern theoretical physics. In this paper we briefly discuss "puzzles" of the black-hole physics, connected with their entropy. We also demonstrate that when the standard energy conditions are violated entropy associated with the event horizon can have quite unexpected behavior.
General geodesic equations of the motion of spinning systems around the (3+1)-dimensional and (2+1)-dimensional rotating anti-de Sitter black holes have been obtained. Based upon these equations, we derived the entropy bound for a rotating system from Kerr-Anti de Sitter black holes and BTZ black holes, respectively. Our result coincides with that of Hod's derived from Kerr black hole, which shows that the entropy bound of the rotating system is neither dependent on the black hole parameters, nor on spacetime dimensions. It is a universal entropy bound.
Recently, Hawking radiation of the black hole has been studied by using the tunnel effect method. It is found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How does the departure from pure thermal spectrum affect the entropy? This is a very interesting problem. In this paper, we calculate the partition function through energy spectrum obtained by using the tunnel effect. From the relation between the partition function and canonical entropy, we can derive the entropy of charged black hole. In our calculation, we consider not only the correction to the b…
Without pretending to any rigour, we find a general expression of the electrostatic self-energy in static black holes with spherical symmetry. We determine the entropy bound of a charged object by assuming the existence of thermodynamics for these black holes. By combining these two results, we show that the entropy bound does not depend on the considered black hole.
It is shown that the classical entropy of the extremal black hole depends on two different limits procedures. If we first take the extremal limit and then the boundary limit, the entropy is zero; if we do it the other way round, we get the Bekenstein-Hawking entropy. By means of the brick wall model, the quantum entropy of scalar field in the extremal black hole background has been calculated for the above two different limits procedures. A possible explanation which considers the quantum effect for the clash of black hole entropy in the extremal limit is given.
Using Relativistic Quantum Geometry we show that the entropy can decrease in very small BHs, under certain circumstances, but always increases in very massive Black-Holes.
The spectroscopy of the apparent horizon of Vaidya black holes is investigated via adiabatic invariance. We obtain an equally spaced entropy spectrum with its quantum equal to the one given by Bekenstein. We demonstrate that the quantization of entropy and area is a generic property of horizon, not only for stationary black holes, and the results also exit in a dynamical black hole. Our work also shows that the quantization of black hole is closely related to Hawking temperature, which is an interesting thing.
A black ring is an asymptotically flat vacuum solution of the Einstein equations with an event horizon of topology $S^1\times S^2$. A connection between the black ring entropy and its Weyl tensor $C_{μνλρ}$ is explored by interpreting the Weyl scalar invariant $C_{μνλρ} C^{μνλρ}$ as the entropy density in 5-dimensional space-time. We calculate the proper volume integral of $C_{μνλρ} C^{μνλρ}$ for a neutral black ring and prove that it is proportional to the entropy of a thin black ring. Similar calculations are extended to more general cases: the black string, the black ring with two angular m…
Based on the generalized uncertainty principle, we study the entropy of a four-dimensional black hole by counting degrees of freedom near the horizon and obtain the (finite) entropy proportional to the surface area at the horizon without a cutoff introduced in the conventional brick-wall method.
We compute logarithmic corrections to entropy for black holes with hyperbolic horizon. For this purpose, we introduce the topological black hole and MTZ black holes in four dimensions, while in five dimensions, the topological black holes and Gauss-Bonnet black hole with negative coupling are considered. As they stand, logarithmic corrections are problematic because small black holes with positive heat capacity have negative energies. However, introducing the background state of extremal black hole, the logarithmic corrections are performed for black hole with hyperbolic horizon.
We introduce the concept of black shell, consisting on a massive thin spherical shell contracting toward its gravitational radius from the point of view of an external observer far from the shell, in order to effectively model the gravitational collapse. Considering complementary description of entanglement entropy of a black shell and according to Gibbons-Hawking Euclidean approach, we calculate the Bekenstein-Hawking entropy retrieving horizon integral and discarding boundary at infinity.
In the Euclidean path integral approach, we calculate the actions and the entropies for the Reissner-Nordström-de Sitter solutions. When the temperatures of black hole and cosmological horizons are equal, the entropy is the sum of one-quarter areas of black hole and cosmological horizons; when the inner and outer black hole horizons coincide, the entropy is only one-quarter area of cosmological horizon; and the entropy vanishes when the two black hole horizons and cosmological horizon coincide. We also calculate the Euler numbers of the corresponding Euclidean manifolds, and discuss the relati…
We propose a way to describe the origin of black hole entropy in the spin foam models of quantum gravity. This stimulates a new way to study the relation of spin foam models and loop quantum gravity.
Membrane method is used to compute the entropy of the NUT-Kerr-Newman black holes. It is found that even though the Euler characteristic is greater than two, the Bekenstein-Hawking area law is still satisfied. The formula $S=χA/8$ relating the entropy and the Euler characteristic becomes inapplicable for non-extreme four dimensional NUT-Kerr-Newman black holes.
Entanglement entropy is often speculated as a strong candidate for the origin of the black-hole entropy. To judge whether this speculation is true or not, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of the black hole entropy. It is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a `thermodynamics of entanglement' by introduc…
We consider corrections to all orders in the Planck length on the quantum state density, and calculate the statistical entropy of the scalar field on the background of the Bardeen regular black hole numerically. We obtain the distribution of entropy which is inside the horizon of black hole and the contribution of the vicinity of horizon takes a great part of the whole entropy.
I discuss a method for obtaining the one-loop quantum corrections to the tree-level entropy for a charged Kerr black hole. Divergences which appear can be removed by renormalization of couplings in the tree-level gravitational action in a manner similar to that for a static black hole.
We explore the entropy spectrum of $(1+1)$ dimensional dilatonic stringy black holes via the adiabatic invariant integral method and the Bohr-Sommerfeld quantization rule. It is found that the corresponding spectrum depends on black hole parameters like charge, ADM mass and more interestingly on the dilatonic field. We calculate the entropy of the present black hole system via the Euclidean treatment of quantum gravity and study the thermodynamics of the black hole and find that the system does not undergo any phase transition.
We compute the entropy of systems of quantum particles satisfying the fractional exclusion statistics in the space-time of 2+1 dimensional black hole by using the brick-wall method. We show that the entropy of each effective quantum field theory with a Planck scale ultraviolet cutoff obeys the area law, irrespective of the angular momentum of the black hole and the statistics interpolating between Bose-Einstein and Fermi-Dirac statistics.
The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether Charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole is one-quarter of the horizon area in f(R) theories coupled to conformally invariant matter. If matter is present that is not conformally invariant the entropy is still proportional to the area of the black hole, but the coefficient is generally not one-quarter. The entropy of black holes in generalized dilaton theories and in theories with Lagrangians that…
Perelman has given a gradient formulation for the Ricci flow, introducing an ``entropy function'' which increases monotonically along the flow.We pursue a thermodynamic analogy and apply Ricci flow ideas to general relativity. We investigate whether Perelman's entropy is related to (Bekenstein-Hawking)geometric entropy as familiar from black hole thermodynamics. From a study of the fixed points of the flow we conclude that Perelman entropy is not connected to geometric entropy. However, we notice that there is a very similar flow which DOES appear to be connected to geometric entropy. The new …
We provide a simple way for calculating the entropy of a Schwarzschild black hole from the entropy of its Hawking radiation. To this end, we show that if a thermodynamic system loses its energy only through the black body radiation, its loss of entropy is always 3/4 of the entropy of the emitted radiation. This proposition enables us to relate the entropy of an evaporating black hole to the entropy of its Hawking radiation. Explicitly, by calculating the entropy of the Hawking radiation emitted in the full period of evaporation of the black hole, we find the Bekenstein-Hawking entropy of the i…
The statistical entropy of a Schwarzschild black string in five dimensions is obtained by counting the black string states which form a representation of the near-horizon conformal symmetry with a central charge. The statistical entropy of the string agrees with its Bekenstein-Hawking entropy as well as that of the Schwarzschild black hole in four dimensions. The choice of the string length which gives the Virasoro algebra also reproduces the precise value of the Bekenstein-Hawking entropy and lies inside the stability bound of the string.
Using brick wall method the entropy of charged dilaton-axion black hole is determined for both asymptotically flat and non-flat cases. The entropy turns out to be proportional to the horizon area of the black hole confirming the Beckenstien, Hawking area-entropy formula for black holes. The leading order logarithmic corrections to the entropy are also derived for such black holes.
We show that in IIB string theory and for D1D5p black holes in ten dimensions the method of entropy function works. Despite the more complicated Wald formula for the entropy of D1D5p black holes in ten dimensions, their entropy is given by entropy function at its extremum point. We use this method for computing the entropy of the system both at the level of supergravity and for its higher order alpha'^3R^4 corrections.
The string-black hole correspondence is considered in the context of the correspondence principle proposed recently by Horowitz and Polchinski. We demonstrate that the entropy of string states and the entropy of a Schwarzschild black hole can be matched including the subleading terms which depend on mass logarithmically. We argue the necessity to include the string interaction (with coupling $g$) in the consideration and propose the $g^2$-dependent modification of the string entropy. The matching of it with the entropy of Schwarzschild black hole is analyzed.
We study the possibility that black hole entropy be identified as entropy of entanglement across the horizon of the vacuum of a quantum field in the presence of the black hole. We argue that a recent proposal for computing entanglement entropy using AdS/CFT holography implies that black hole entropy can be exactly equated with entanglement entropy. The implementation of entanglement entropy in this context solves all the problems (such as cutoff dependence and the species problem) typically associated with this identification.
We point out that the entropy of (near) extremal black holes can be interpreted as the entanglement entropy of dual conformal quantum mechanics via AdS2/CFT1. As an explicit example, we study near extremal BTZ black holes and derive this claim from AdS3/CFT2. We also analytically compute the entanglement entropy in the two dimensional CFT of a free Dirac fermion compactified on a circle at finite temperature. From this result, we clarify the relation between the thermal entropy and entanglement entropy, which is essential for the entanglement interpretation of black hole entropy.
Here we explain how C. Tsallis' reply (Entropy 2021, 23(5), 630) fails to respond to points raised in (Entropy 2020, 22(10), 1110) and introduces further inconsistencies on the origin of black hole entropy. In his reply, Tsallis argues that the extensivity of thermodynamical entropy with respect to chosen variables needs to be preserved. Consequently the entropy functional is inadequate for black holes. Here we explain the undesirable consequences of this reasoning on black hole thermodynamics.
In this work, we examine the entropy emission property of black holes. When the greybody factor is considered, it is found that Schwarzschild black hole is a one-dimensional entropy emitter, which is independent of the spacetime dimension and the spin of the emitted quanta. However, when generalized to other black holes with two or more parameters, the result shows that the one-dimensional entropy emission property will be violated. Thus our result implies that not all black holes behave as one-dimensional entropy emitters.
