Black hole entropy quantization
Corichi, A; Fernandez-Borja, E; Corichi, Alejandro; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2006-01-01
Ever since the pioneer works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is not quantized in equidistant steps can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show that an observed oscillatory behavior in the entropy-area relation, when properly interpreted yields an entropy that has discrete, equidistant values that are consistent with the Bekenstein framework.
Hayward, Sean A.; Mukohyama, Shinji; Ashworth, M. C.
1998-01-01
We consider two non-statistical definitions of entropy for dynamic (non-stationary) black holes in spherical symmetry. The first is analogous to the original Clausius definition of thermodynamic entropy: there is a first law containing an energy-supply term which equals surface gravity times a total differential. The second is Wald's Noether-charge method, adapted to dynamic black holes by using the Kodama flow. Both definitions give the same answer for Einstein gravity: one-quarter the area ...
Comparisons of Black Hole Entropy
Kupferman, Judy
2016-01-01
In this thesis I examine several different concepts of black hole entropy in order to understand whether they describe the same quantity. I look at statistical and entanglement entropies, Wald entropy and Carlip's entropy from conformal field theory, and compare their behavior in a few specific aspects: divergence at the BH horizon, dependence on space time curvature and behavior under a geometric variation. I find that statistical and entanglement entropy may be similar but they seem to differ from the entropy of Wald and Carlip. Chapters 2 and 3 overlap with 1010.4157 and 1310.3938. Chapter 4 does not appear elsewhere.
Entanglement Entropy of Black Holes
Directory of Open Access Journals (Sweden)
Sergey N. Solodukhin
2011-10-01
Full Text Available The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the black-hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
How objective is black hole entropy?
Lau, Y K
1994-01-01
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 of negligible relative mass fluctutation. {}From the information theoretic perspective, the example of a Schwarzchild black hole seems to suggest that black hole entropy is no different from ordinary thermodynamic entropy. It is a property of the experimental data of a black hole, rather than being an intrinsic physical property of a black hole itself independent of any observer. However, it is still weakly objective in...
Entanglement Entropy of Black Holes
Solodukhin, Sergey N.
2011-12-01
The entanglement entropy is a fundamental quantity, which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff, which regulates the short-distance correlations. The geometrical nature of entanglement-entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black-hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ’t Hooft’s brick-wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields, which non-minimally couple to gravity, is emphasized. The holographic description of the entanglement entropy of the blackhole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein-Hawking entropy entirely as the entanglement entropy.
Black hole entropy and entropy of entanglement
Kabat, D
1995-01-01
We compute the one-loop correction to the entropy of a very massive black hole, by evaluating the partition function in the presence of a conical singularity for quantum fields of spin zero, one-half, and one. We compare the results to the entropy of entanglement, defined by the density matrix which describes the ground state of the field as seen from one side of a boundary in Minkowski space. Fields of spin zero and one-half contribute an entropy to the black hole which is identical to their entropy of entanglement. For spin one a contact interaction with the horizon appears in the black hole entropy but is absent from the entropy of entanglement. Expressed as a particle path integral the contact term is an integral over paths which begin and end on the horizon; it is the field theory limit of the interaction proposed by Susskind and Uglum which couples a closed string to an open string stranded on the horizon.
Black Hole Entropy from Entropy of Hawking Radiation
Aghapour, Sajad
2016-01-01
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 initial black hole.
Entropy of Quantum Black Holes
Directory of Open Access Journals (Sweden)
Romesh K. Kaul
2012-02-01
Full Text Available In the Loop Quantum Gravity, black holes (or even more general Isolated Horizons are described by a SU(2 Chern-Simons theory. There is an equivalent formulation of the horizon degrees of freedom in terms of a U(1 gauge theory which is just a gauged fixed version of the SU(2 theory. These developments will be surveyed here. Quantum theory based on either formulation can be used to count the horizon micro-states associated with quantum geometry fluctuations and from this the micro-canonical entropy can be obtained. We shall review the computation in SU(2 formulation. Leading term in the entropy is proportional to horizon area with a coefficient depending on the Barbero-Immirzi parameter which is fixed by matching this result with the Bekenstein-Hawking formula. Remarkably there are corrections beyond the area term, the leading one is logarithm of the horizon area with a definite coefficient −3/2, a result which is more than a decade old now. How the same results are obtained in the equivalent U(1 framework will also be indicated. Over years, this entropy formula has also been arrived at from a variety of other perspectives. In particular, entropy of BTZ black holes in three dimensional gravity exhibits the same logarithmic correction. Even in the String Theory, many black hole models are known to possess such properties. This suggests a possible universal nature of this logarithmic correction.
Black Hole Entropy without Brick Walls
Demers, J. -G.; Lafrance, R.; Myers, R. C.
1995-01-01
We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula, $S=\\A/(4G)$. Our calculation also yields a constant contribution to the black hole entropy, a contr...
Quantum aspects of black hole entropy
Indian Academy of Sciences (India)
Parthasarathi Majumdar
2000-10-01
This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical perspective. Quantum corrections to the semiclassical Bekenstein–Hawking area law for black hole entropy, obtained within the quantum geometry framework, are treated in some detail. Their ramiﬁcation for the holographic entropy bound for bounded stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based = 2 supergravity are also discussed, albeit more brieﬂy.
Black hole entropy in loop quantum gravity
Agulló, Iván; Barbero G, J. Fernando; Borja, E. F.; Díaz-Polo, Jacobo; Villaseñor, Eduardo J. S.
2012-05-01
We discuss the recent progress on black hole entropy in loop quantum gravity, focusing in particular on the recently discovered discretization effect for microscopic black holes. Powerful analytical techniques have been developed to perform the exact computation of entropy. A statistical analysis of the structures responsible for this effect shows its progressive damping and eventual disappearance as one increases the considered horizon area.
Black hole entropy and the renormalization group
Satz, Alejandro
2013-01-01
Four decades after its first postulation by Bekenstein, black hole entropy remains mysterious. It has long been suggested that the entanglement entropy of quantum fields on the black hole gravitational background should represent at least an important contribution to the total Bekenstein-Hawking entropy, and that the divergences in the entanglement entropy should be absorbed in the renormalization of the gravitational couplings. In this talk, we describe how an improved understanding of black hole entropy is obtained by combining these notions with the renormalization group. By introducing an RG flow scale, we investigate whether the total entropy of the black hole can be partitioned in a "gravitational" part related to the flowing gravitational action, and a "quantum" part related to the unintegrated degrees of freedom. We describe the realization of this idea for free fields, and the complications and qualifications arising for interacting fields.
Holographic actions from black hole entropy
Caravelli, Francesco; Modesto, Leonardo
2010-01-01
Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. Our point of view is to consider fundamental the black hole entropy and the action an emerged object. We then specialize to a particular class of effective theories: the f(R) theories. We apply the idea, using a simple mind ansatz,...
Black hole entropy without brick walls
Demers, Jean-Guy; Lafrance, René; Myers, Robert C.
1995-08-01
We present evidence which confirms a suggestion by Susskind and Uglum regarding black hole entropy. Using a Pauli-Villars regulator, we find that 't Hooft's approach to evaluating black hole entropy through a statistical-mechanical counting of states for a scalar field propagating outside the event horizon yields precisely the one-loop renormalization of the standard Bekenstein-Hawking formula S=scrA/(4G). Our calculation also yields a constant contribution to the black hole entropy, a contribution associated with the one-loop renormalization of higher curvature terms in the gravitational action.
Black hole entropy in two dimensions
Myers, R C
1994-01-01
Black hole entropy is studied for an exactly solvable model of two-dimensional gravity\\cite{rst1}, using recently developed Noether charge techniques\\cite{wald1}. This latter approach is extended to accomodate the non-local form of the semiclassical effective action. In the two-dimensional model, the final black hole entropy can be expressed as a local quantity evaluated on the horizon. This entropy is shown to satisfy an increase theorem on either the global or apparent horizon of a two-dimensional black hole.
Black Hole Radiation and Volume Statistical Entropy
Rabinowitz, M
2005-01-01
The simplest possible equations for Hawking radiation, and other black hole radiated power is derived in terms of black hole density. Black hole density also leads to the simplest possible model of a gas of elementary constituents confined inside a gravitational bottle of Schwarzchild radius at tremendous pressure, which yields identically the same functional dependence as the traditional black hole entropy. Variations of Sbh are can be obtained which depend on the occupancy of phase space cells. A relation is derived between the constituent momenta and the black hole radius RH
Black hole versus cosmological horizon entropy
Davis, T M; Lineweaver, C H; Davis, Tamara M.; Lineweaver, Charles H.
2003-01-01
The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson-Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models show an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds.
Black hole versus cosmological horizon entropy
International Nuclear Information System (INIS)
The generalized second law of thermodynamics states that entropy always increases when all event horizons are attributed with an entropy proportional to their area. We test the generalized second law by investigating the change in entropy when dust, radiation and black holes cross a cosmological event horizon. We generalize for flat, open and closed Friedmann-Robertson-Walker universes by using numerical calculations to determine the cosmological horizon evolution. In most cases, the loss of entropy from within the cosmological horizon is more than balanced by an increase in cosmological event horizon entropy, maintaining the validity of the generalized second law of thermodynamics. However, an intriguing set of open universe models shows an apparent entropy decrease when black holes disappear over the cosmological event horizon. We anticipate that this apparent violation of the generalized second law will disappear when solutions are available for black holes embedded in arbitrary backgrounds
Kerr Black Hole Entropy and its Quantization
Jiang, Ji-Jian; Li, Chuan-An; Cheng, Xie-Feng
2016-08-01
By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al.
Scaling Behavior of Black Hole Entropy
Schimmrigk, R
2000-01-01
It is shown that the entropy of fourdimensional black holes in string theory compactified on weighted Calabi-Yau hypersurfaces shows scaling behavior in a certain limit. This leads to non-monotonic functions on the moduli space.
Holographic actions from black hole entropy
Caravelli, Francesco
2010-01-01
Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. Our point of view is to consider fundamental the black hole entropy and the action an emerged object. We then specialize to a particular class of effective theories: the f(R) theories. We apply the idea, using a simple mind ansatz, to loop quantum gravity and to a general class of log-corrected entropy formulas.
Entropy Inequality Violations from Ultraspinning Black Holes.
Hennigar, Robie A; Mann, Robert B; Kubizňák, David
2015-07-17
We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold. PMID:26230779
Entropy Inequality Violations from Ultraspinning Black Holes.
Hennigar, Robie A; Mann, Robert B; Kubizňák, David
2015-07-17
We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.
Gravity Quanta, Entropy and Black Holes
Alfonso-Faus, A
1999-01-01
We propose the use of a gravitational uncertainty principle for gravitation.We define the corresponding gravitational Planck's constant and thegravitational quantum of mass. We define entropy in terms of the quantum ofgravity with the property of having an extensive quality. The equivalent 2ndlaw of thermodynamics is derived, the entropy increasing linearly withcosmological time. These concepts are applied to the case of black holes,finding their entropy and discussing their radiation.
Quantum statistical entropy for Kerr-de Sitter black hole
Institute of Scientific and Technical Information of China (English)
Zhang Li-Chun; Wu Yue-Qin; Zhao Ren
2004-01-01
Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.
Quantum Entropy of Black Hole with Internal Global Monopole
Institute of Scientific and Technical Information of China (English)
HAN Yi-Wen; YANG Shu-Zheng; LIU Wen-Biao
2005-01-01
Using the generalized uncertainty relation, the new equation of state density is obtained, and then the entropy of black hole with an internal global monopole is discussed. The divergence that appears in black hole entropy calculation through original brick-wall model is overcome. The result of the direct proportion between black hole entropy and its event horizon area is drawn and given. The result shows that the black hole entropy must be the entropy of quantum state near the event horizon.
Entropy Correction for Kerr Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Sheng-Li
2005-01-01
In this paper, we discuss leading-order corrections to the entropy of Kerr black hole due to thermal fluctuations in the finite cavity. Then temperature is constant, the solution of the black hole is obtained within a cavity, that is, the solution of the spacetime after considering the radiation of the black hole. Therefore, we derive that the location of the black hole horizon and specific heat are the functions of temperature and the radius of the cavity.Corrections to entropy also are related to the radius of the cavity. Through calculation, we obtain conditions of taking the value of the cavity's radius. We provide a new way for studying the corrections of complicated spacetimes.
Symmetry and entropy of black hole horizons
Dreyer, O; Smolin, L; Dreyer, Olaf; Markopoulou, Fotini; Smolin, Lee
2004-01-01
We argue, using methods taken from the theory of noiseless subsystems in quantum information theory, that the quantum states associated with a Schwarzchild black hole live in the restricted subspace of the Hilbert space of horizon boundary states in which all punctures are equal. Consequently, one value of the Immirzi parameter matches both the Hawking value for the entropy and the quasi normal mode spectrum of the Schwarzchild black hole.
Entropy of Intermediate-Mass Black Holes
Frampton, Paul H.
2009-01-01
Observational searches for Intermediate-Mass Black Holes (IMBHs), defined to have masses between 30 and 300,000 solar masses, provide limits which allow up to ten percent of what is presently identified as halo dark matter to be in the form of IMBHs. These concentrate entropy so efficiently that the halo contribution can be bigger than the core supermassive black hole. Formation of IMBHs is briefly discussed.
Quantum geometry and microscopic black hole entropy
Energy Technology Data Exchange (ETDEWEB)
Corichi, Alejandro [Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A Postal 61-3, Morelia, Michoacan 58090 (Mexico); DIaz-Polo, Jacobo [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Fernandez-Borja, Enrique [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2007-01-07
Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that is consistent with a black hole of a given horizon area A{sub 0} are counted and the statistical entropy, as a function of the area, is obtained for A{sub 0} up to 550l{sup 2}{sub Pl}. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to {gamma} = 0.274, which has been previously obtained analytically. However, a new and oscillatory functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.
Black hole entropy in higher curvature gravity
Jacobson, T; Myers, R C; Jacobson, Ted; Kang, Gungwon; Myers, Robert C
1995-01-01
We discuss some recent results on black hole thermodynamics within the context of effective gravitational actions including higher-curvature interactions. Wald's derivation of the First Law demonstrates that black hole entropy can always be expressed as a local geometric density integrated over a space-like cross-section of the horizon. In certain cases, it can also be shown that these entropy expressions satisfy a Second Law. One such simple example is considered from the class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar.
Dirty black holes Entropy versus area
Visser, M
1993-01-01
Considerable interest has recently been expressed in the entropy versus area relationship for ``dirty'' black holes --- black holes in interaction with various classical matter fields, distorted by higher derivative gravity, or infested with various forms of quantum hair. In many cases it is found that the entropy is simply related to the area of the event horizon: S = k A_H/(4\\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for: Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of (Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair. The pattern underlying these results is less than clear. This paper systematizes these results by deriving a general formula for the entropy: S = {k A_H/(4\\ell_P^2)} + {1/T_H} \\int_\\Sigma [rho - {L}_E ] K^\\mu d\\Sigma_\\mu + \\int_\\Sigma s V^\\mu d\\Sigma_\\mu. (K^\\mu is the timelike Killing vector, V^\\mu the four velocity of a co--rotating o...
On Black Hole Entropy Corrections in the Grand Canonical Ensemble
Mahapatra, Subhash; Sarkar, Tapobrata
2011-01-01
We study entropy corrections due to thermal fluctuations for asymptotically AdS black holes in the grand canonical ensemble. To leading order, these can be expressed in terms of the black hole response coefficients via fluctuation moments. We also analyze entropy corrections due to mass and charge fluctuations of R-charged black holes, and our results indicate an universality in the logarithmic corrections to charged AdS black hole entropy in various dimensions.
Loop quantum gravity and black hole entropy quantization
Institute of Scientific and Technical Information of China (English)
LI ChuanAn; JIANG JiJian; SU JiuQing
2009-01-01
Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity, the minimum horizon area gap is obtained. Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization. The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.
Loop quantum gravity and black hole entropy quantization
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.
Effects of Noncommutativity on the Black Hole Entropy
Gupta, Kumar S.(Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India); Harikumar, E.; Tajron Jurić; Stjepan Meljanac; Andjelo Samsarov
2013-01-01
In this paper the BTZ black hole geometry is probed with a noncommutative scalar field which obeys the $\\kappa$-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton's constant due...
Black Hole Entropy, Topological Entropy and Noncommutative Geometry
Zois, Ioannis P.
2001-01-01
Foliated manifolds are particular examples of noncommutative spaces. In this article we try to give a qualitative description of the Godbillon-Vey class and its relation on the one hand to the holonomy and on the other hand to the topological entropy of a foliation, using a remarkable theorem proved recently by G. Duminy relating these three notions in the case of codim-1 foliations. Moreover we shall investigate its possible relation with the black hole entropy adopting the superstring theor...
Black Holes, Mergers, and the Entropy Budget of the Universe
Kephart, Thomas W.; Ng, Y. Jack
2002-01-01
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 eventuall...
Canonical Entropy and Phase Transition of Rotating Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun
2008-01-01
Recently, the Hawking radiation of a black hole has been studied using the tunnel effect method. The radiation spectrum of a black hole is derived. By discussing the correction to spectrum of the rotating black hole, we obtain the canonical entropy. The derived canonical entropy is equal to the sum of Bekenstein-Hawking entropy and correction term. The correction term near the critical point is different from the one near others. This difference plays an important role in studying the phase transition of the black hole. The black hole thermal capacity diverges at the critical point. However, the canonical entropy is not a complex number at this point. Thus we think that the phase transition created by this critical point is the second order phase transition. The discussed black hole is a five-dimensional Kerr-AdS black hole. We provide a basis for discussing thermodynamic properties of a higher-dimensional rotating black hole.
Quantum Statistical Entropy of Five-Dimensional Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li
2006-01-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
Correction value to charged Bekenstein-Hawking black hole entropy
Institute of Scientific and Technical Information of China (English)
ZHANG LiChun; WU YueQin; ZHAO Ren
2008-01-01
Recently, based on the study of black hole Hawking radiation with the tunnel effect method, we found that the radiation spectrum of the black hole is not a strict pure thermal spectrum. It is a very interesting problem to determine how the departure of the black hole radiation spectrum from the pure thermal spectrum affects entropy. We calculate the partition function by the energy spectrum obtained using tunnel effect. Using the relation between the partition function and entropy, we derive the correction value to Bekenstein-Hawking entropy of the charged black hole. Furthermore, we obtain the conditions that various thermodynamic quantities must satisfy, when phase transition of the charged black hole occurs.
Gravitational correlation, black hole entropy and information conservation
He, Dongshan
2016-01-01
When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by E. Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.
Scalar fields in BTZ black hole spacetime and entanglement entropy
Veer Singh, Dharm; Siwach, Sanjay
2013-12-01
We study the quantum scalar fields in the background of BTZ black hole spacetime. We calculate the entanglement entropy using the discretized model, which resembles a system of coupled harmonic oscillators. The leading term of the entropy formula is standard Bakenstein-Hawking entropy and sub-leading corresponds to quantum corrections to black hole entropy. We calculate the coefficient of sub-leading logarithmic corrections numerically.
Black hole entropy and finite geometry
International Nuclear Information System (INIS)
It is shown that the E6(6) symmetric entropy formula describing black holes and black strings in D=5 is intimately tied to the geometry of the generalized quadrangle GQ(2, 4) with automorphism group the Weyl group W(E6). The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ(2, 4). Different truncations with 15, 11 and 9 charges are represented by three distinguished subconfigurations of GQ(2, 4), well known to finite geometers; these are the 'doily'[i.e. GQ(2, 2)] with 15, the 'perp set' of a point with 11, and the 'grid'[i.e. GQ(2, 1)] with nine points, respectively. In order to obtain the correct signs for the terms in the entropy formula, we use a noncommutative labeling for the points of GQ(2, 4). For the 40 different possible truncations with nine charges this labeling yields 120 Mermin squares--objects well known from studies concerning Bell-Kochen-Specker-like theorems. These results are connected to our previous ones obtained for the E7(7) symmetric entropy formula in D=4 by observing that the structure of GQ(2, 4) is linked to a particular kind of geometric hyperplane of the split Cayley hexagon of order 2, featuring 27 points located on nine pairwise disjoint lines (a distance-3-spread). We conjecture that the different possibilities of describing the D=5 entropy formula using Jordan algebras, qubits and/or qutrits correspond to employing different coordinates for an underlying noncommutative geometric structure based on GQ(2, 4).
Black Hole Entropy and Finite Geometry
Lévay, Péter; Vrana, Péter; Pracna, Petr
2009-01-01
It is shown that the $E_{6(6)}$ symmetric entropy formula describing black holes and black strings in D=5 is intimately tied to the geometry of the generalized quadrangle GQ$(2,4)$ with automorphism group the Weyl group $W(E_6)$. The 27 charges correspond to the points and the 45 terms in the entropy formula to the lines of GQ$(2,4)$. Different truncations with $15, 11$ and 9 charges are represented by three distinguished subconfigurations of GQ$(2,4)$, well-known to finite geometers; these are the "doily" (i. e. GQ$(2,2)$) with 15, the "perp-set" of a point with 11, and the "grid" (i. e. GQ$(2,1)$) with 9 points, respectively. In order to obtain the correct signs for the terms in the entropy formula, we use a non- commutative labelling for the points of GQ$(2,4)$. For the 40 different possible truncations with 9 charges this labelling yields 120 Mermin squares -- objects well-known from studies concerning Bell-Kochen-Specker-like theorems. These results are connected to our previous ones obtained for the $E_...
Black hole entropy in the O(N) model
Kabat, D; Strassler, M J
1995-01-01
We consider corrections to the entropy of a black hole from an O(N) invariant linear \\s-model. We obtain the entropy from a 1/N expansion of the partition function on a cone. The entropy arises from diagrams which are analogous to those introduced by Susskind and Uglum to explain black hole entropy in string theory. The interpretation of the \\sm entropy depends on scale. At short distances, it has a state counting interpretation, as the entropy of entanglement of the N fields \\pa. In the infrared, the effective theory has a single composite field \\s \\sim \\pa \\pa, and the state counting interpretation of the entropy is lost.
Effects of Noncommutativity on the Black Hole Entropy
Gupta, Kumar S; Juric, Tajron; Meljanac, Stjepan; Samsarov, Andjelo
2013-01-01
In this paper the BTZ black hole geometry is probed with a noncommutative scalar field which obeys the $\\kappa$-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton's constant due to the effects of the noncommutativity.
Effects of Noncommutativity on the Black Hole Entropy
International Nuclear Information System (INIS)
The BTZ black hole geometry is probed with a noncommutative scalar field which obeys the κ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity
Effects of Noncommutativity on the Black Hole Entropy
Directory of Open Access Journals (Sweden)
Kumar S. Gupta
2014-01-01
Full Text Available The BTZ black hole geometry is probed with a noncommutative scalar field which obeys the κ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.
Quantum correction to the entropy of noncommutative BTZ black hole
Anacleto, M A; Passos, E; Cavalcanti, A G; Spinelly, J
2015-01-01
In this paper we consider the generalized uncertainty principle (GUP) in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for noncommutative BTZ black hole. In our results we obtain several types of corrections including the expected logarithmic correction to the area entropy associated with the noncommutative BTZ black holes.
Entropy of the Kerr–Sen black hole
Indian Academy of Sciences (India)
Alexis Larrañaga
2011-04-01
We study the entropy of Kerr–Sen black hole of heterotic string theory beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the ﬁrst law of thermodynamics, we derive the corrections to the entropy of the black hole. The leading (logarithmic) and non-leading corrections to the area law are obtained.
Deformed Density Matrix and Quantum Entropy of the Black Hole
Directory of Open Access Journals (Sweden)
A. E. Shalyt-Margolin
2006-03-01
Full Text Available In the present work the approach - density matrix deformation - earlier developed by the author to study a quantum theory of the Early Universe (Planck's scales is applied to study a quantum theory of black holes. On this basis the author investigates the information paradox problem, entropy of the black hole remainders after evaporation, and consistency with the holographic principle. The possibility for application of the proposed approach to the calculation of quantum entropy of a black hole is considered.
Entropy correction of BTZ black holes in a tunneling framework
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, using the Parikh-Wilczek tunneling framework, we first calculate the emission rates of non-rotating BTZ black holes and rotating BTZ black holes to second order accuracy. Then, by assuming that the emission process satisfies an underlying unitary theory, we obtain the corrected entropy of the BTZ black holes. A log term emerges naturally in the expression of the corrected entropy. A discussion about the inverse area term is also presented.
Statistical entropy of Calabi-Yau black holes
Iofa, Mikhail Z.; Pando Zayas, Leopoldo A.
1999-03-01
We compute the statistical entropy of nonextremal 4D and extremal 5D Calabi-Yau black holes and find exact agreement with the Bekenstein-Hawking entropy. The computation is based on the fact that the near-horizon geometry of equivalent representations contains as a factor the Bañados-Teitelboim-Zanelli black hole and on subsequent use of Strominger's proposal generalizing the statistical count of microstates of the BTZ black hole due to Carlip.
The information entropy of a static dilaton black hole
Institute of Scientific and Technical Information of China (English)
2008-01-01
In accordance with holographic principle, by calculating the statistical entropy of the quantum field just at the event horizon of the Garfinkle-Horowitz-Strominger dilaton black hole, the information entropy of the black hole was investigated and the Bekenstein-Hawking formula was obtained. The results show that black hole entropy is identical with the statistical entropy of the quantum field at the horizon. Using the generalized uncertainty relation, the divergence of the state density near the event horizon in usual quantum field theory was removed, and the cutoffs and the little mass approximation in the heat gas method of black hole entropy were avoided. Thus, the microstates of the massive scalar field just at the event horizon of the static dilaton black hole were studied directly and a description on holograph principle was presented. By using residue theorem, the integral difficulty in the calculation was overcome, and the information entropy and the Bekenstein-Hawking formula were obtained quantitatively. Compared with the black hole entropy from the loop quantum gravity, the consistency of methods and results of calculating black hole entropy in non-commutative quantum field theory and loop quantum gravity was investigated. By this, the gravity correction constant in the generalized uncertainty relation was suggested and the sense of holographic principle was discussed.
Entropy bound of horizons for charged and rotating black holes
International Nuclear Information System (INIS)
We revisit the entropy product, entropy sum and other thermodynamic relations of charged and rotating black holes. Based on these relations, we derive the entropy (area) bound for both event horizon and Cauchy horizon. We establish these results for variant class of 4-dimensional charged and rotating black holes in Einstein(–Maxwell) gravity and higher derivative gravity. We also generalize the discussion to black holes with NUT charge. The validity of this formula, which seems to be universal for black holes with two horizons, gives further clue on the crucial role that the thermodynamic relations of multi-horizons play in black hole thermodynamics and understanding the entropy at the microscopic level
Correction value to charged Bekenstein-Hawking black hole entropy
Institute of Scientific and Technical Information of China (English)
2008-01-01
Recently,based on the study of black hole Hawking radiation with the tunnel effect method,we found that the radiation spectrum of the black hole is not a strict pure thermal spectrum. It is a very interesting problem to determine how the departure of the black hole radiation spectrum from the pure thermal spectrum affects entropy. We calculate the partition function by the energy spectrum obtained using tunnel effect. Using the relation between the partition function and entropy,we derive the correction value to Bekenstein-Hawking entropy of the charged black hole. Fur-thermore,we obtain the conditions that various thermodynamic quantities must satisfy,when phase transition of the charged black hole occurs.
Statistical Entropy of Four-Dimensional Extremal Black Holes
Maldacena, Juan; Strominger, Andrew
1996-01-01
String theory is used to count microstates of four-dimensional extremal black holes in compactifications with $N=4$ and $N=8$ supersymmetry. The result agrees for large charges with the Bekenstein-Hawking entropy.
Black-hole thermodynamics: Entropy, information and beyond
Indian Academy of Sciences (India)
Saurya Das
2004-10-01
We review some recent advances in black-hole thermodynamics including statistical mechanical origins of black-hole entropy and its leading order corrections from the view points of various quantum gravity theories. We then examine the problem of information loss and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.
Quantum Black Hole Entropy and Localization in Supergravity
Reys, V.
2016-01-01
In this thesis, we examine in detail the notion of black hole entropy in Quantum Field Theories, with a specific focus on supersymmetric black holes and the perturbative and non-perturbative quantum corrections to the classical area-law of Bekenstein-Hawking, where the latter stipulates that the the
Renormalized Thermodynamic Entropy of Black Holes in Higher Dimensions
Kim, Sang Pyo; Kim, Sung Ku; Soh, Kwang-Sup; Yee, Jae Hyung
1996-01-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstr\\"{o}m black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular we show that the matter field contribution in odd dimens...
Entropy Corrections for a Charged Black Hole of String Theory*
Institute of Scientific and Technical Information of China (English)
Alexis Larra(n)aga
2011-01-01
We study the entropy of the Gibbons-Macda-Garfinkle-Horowitz-Strominger (GMGHS) charged black hole, originated from the effective action that emerges in the low-energy of string theory, beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics ve derive the quantum corrections to the entropy of the black hole. The leading (logarithmic) and non leading corrections to the area law are obtained.
Black hole entropy, loop gravity, and polymer physics
Energy Technology Data Exchange (ETDEWEB)
Bianchi, Eugenio, E-mail: bianchi@cpt.univ-mrs.fr [Centre de Physique Theorique de Luminy , case 907, F-13288 Marseille (France)
2011-06-07
Loop gravity provides a microscopic derivation of black hole entropy. In this paper, I show that the microstates counted admit a semiclassical description in terms of shapes of a tessellated horizon. The counting of microstates and the computation of the entropy can be done via a mapping to an equivalent statistical mechanical problem: the counting of conformations of a closed polymer chain. This correspondence suggests a number of intriguing relations between the thermodynamics of black holes and the physics of polymers.
Entanglement Entropy of AdS Black Holes
Directory of Open Access Journals (Sweden)
Maurizio Melis
2010-11-01
Full Text Available We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two- and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.
Renormalized thermodynamic entropy of black holes in higher dimensions
Kim, Sang Pyo; Kim, Sung Ku; Soh, Kwang-Sup; Yee, Jae Hyung
1997-02-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordström black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon.
Renormalized thermodynamic entropy of black holes in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Kim, S.P. [Department of Physics, Kunsan National University, Kunsan 573-701 (Korea); Kim, S.K. [Department of Physics, Ewha Womans University, Seoul 120-750 (Korea); Soh, K. [Department of Physics Education, Seoul National University, Seoul 151-742 (Korea); Yee, J.H. [Department of Physics and Institute for Mathematical Sciences, Yonsei University, Seoul 120-749 (Korea)
1997-02-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstr{umlt o}m black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. {copyright} {ital 1997} {ital The American Physical Society}
Statistical Entropy of Horowitz-Strominger Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Jun-Fang; ZHANG Li-Chun
2002-01-01
The partition functions of bosonic and fermionic fields in Horowitz Strominger black hole are deriveddirectly by quantum statistical method. Then via the improved brick-wall method (membrane model), the statisticalentropy of black hole is obtained. If a proper parameter is chosen in our result, it is found out that the entropy isproportional to the area of horizon. The stripped term and the divergent logarithmic term in the original brick-wallmethod no longer exist. The difficulty in solving the wave equations of scalar and Dirac fields is avoided. A new neatway of calculating the entropy of various complicated black holes is offered.
Horowitz-Strominger Black Hole Entropy Without Brick Wall
Institute of Scientific and Technical Information of China (English)
ZHANG Li-Chun; ZHAO Ren; LIN Hai
2004-01-01
@@ A Horowitz-Strominger black hole is discussed through a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst in the last stage of emission from a HorowitzStrominger black hole. When the new equation of state density is used to investigate the entropy of bosonic field and fermionic field outside the horizon of a static Horowitz-Strominger black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution in the vicinity of the horizon.
Holographic Entropy Bound of a Nonstationary Black Hole
Institute of Scientific and Technical Information of China (English)
LIU Cheng-Zhou
2006-01-01
@@ In accordance with the holographic principle, by counting the states of the scalar field just at the event horizon of the Vaidya-Bonner black hole, the holographic entropy bound of the black hole is calculated and the BekensteinHawking formula is obtained. With the generalized uncertainty principle, the divergence of statedensity at event horizon in the ordinary quantum field theory is removed. With the residue theorem, the integral trouble in the calculation is overcome. The present result is quantitatively tenable and the holographic principle is realized by applying the quantum field theory to the black hole entropy problem. Compared with some previous works, it is suggested that the quantum states contributing to black hole entropy should be restricted on the event horizon.
Microscopic Entropy of N=2 Extremal Black Holes
David M. Kaplan; Lowe, David A.; Maldacena, Juan M.; Strominger, Andrew
1996-01-01
String theory is used to compute the microscopic entropy for several examples of black holes in compactifications with $N=2$ supersymmetry. Agreement with the Bekenstein-Hawking entropy and the moduli-independent $N=2$ area formula is found in all cases.
Entropy of Reissner-Nordstr\\"om-de Sitter black hole
Zhang, Li-Chun; Ma, Meng-Sen
2016-01-01
Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordstr\\"om black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tends to coincide.
Information entropy for static spherically symmetric black holes
Institute of Scientific and Technical Information of China (English)
Jiang Ji-Jian; Li Chuan-An
2009-01-01
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein-Hawking entropy when the suitable cutoff factor is adopted.
Finiteness of Entanglement Entropy in Quantum Black Hole
Wen, Wen-Yu
2015-01-01
In the \\cite{Kuwakino:2014nra}, a logarithmic correction to the Bekenstein-Hawking entropy was suggested to act as the entanglement entropy which encodes the black hole information. A sudden entanglement model of CFT within finite Euclidean time was proposed and justified by the alternative sign for $n$-partite quantum information. However, this prelimary form suffers from the notorious divergence at its low temperature limit. In this letter, we propose a modified form for black hole entanglement entropy such that the divergence sickness can be cured. We discuss its asymptotic form at both IR and UV limit and relation to the higher loop quantum correction. At last, we argue that the black hole remnant hypothesis may not be needed for this modified entanglement entropy.
Gravitational entropy of a Schwarzschild-type black hole
Dil, Emre
2016-07-01
In this study, Clifton, Ellis and Tavakol's gravitational entropy proposal is used to determine the entropy of free gravitational fields due to a spherical symmetric Schwarzschild-type black hole which is considered in the framework of f( R) gravity. In order to obtain the gravitational entropy, we calculate the Weyl tensor of the black hole to determine the Bel-Robinson tensor, giving the super energy density. By using the super energy density, we obtain the gravitational energy density and the gravitational temperature to calculate the gravitational entropy of the f( R) gravity black hole. This proposal can reproduce the Bekenstein-Hawking value in general relativity limit, but cannot reproduce it in the f( R) gravity case.
Entropy of three-dimensional BTZ black holes
Institute of Scientific and Technical Information of China (English)
GAO; Changjun; SHEN; Yougen
2004-01-01
The entropies of scalar field and neutrino field are calculated in the back ground of three-dimensional BTZ black hole.Considering statistical physics,we propose not to consider the superraradiant modes for bosons(Fermion fields do not displaysup perradiance).In fact,the nonsuperradiant modes do contribute exactly the area entropy for both bosons and fermions.The result shows that the neutrino field entropy is 3/2 times the scalar one.
Entropy of N-Dimensional Spherically Symmetric Charged Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun
2003-01-01
By using the method of quantum statistics, we derive directly the partition functions of bosonic andfermionic fields in the N-dimensional spherically symmetric charged black hole space-time. The statistical entropy ofblack hole is obtained by an improved brick-wall method. When we choose proper parameters in our results, we canobtain that the entropy of black hole is proportional to the area of horizon. In our result, there do not exist neglectedterm and divergent logarithmic term given in the original brick-wall method. We avoid the difficulty in solving the waveequation of scalar and Dirac fields. We offer a simple and direct way of studying entropy of the higher-dimensional black hole.
Universal Near-Horizon Conformal Structure and Black Hole Entropy
Chakrabarti, Sayan K.; Gupta, Kumar S.; Sen, Siddhartha
It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes in our formalism can be identified with the FLM model, although not through the AdS/CFT correspondence. The corresponding entropy for the BTZ provides a lower bound for the entropy of this entire class of black holes.
Entropy calculation for a toy black hole
Sahlmann, H.
2008-01-01
In this note we carry out the counting of states for a black hole in loop quantum gravity, however assuming an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a
Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory
Zois, Ioannis P.
2001-01-01
We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.
Loop quantum gravity and Planck-size black hole entropy
Corichi, A; Fernandez-Borja, E; Corichi, Alejandro; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2007-01-01
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.
Loop quantum gravity and Planck-size black hole entropy
Energy Technology Data Exchange (ETDEWEB)
Corichi, Alejandro [Instituto de Matematicas, Unidad Morelia, Universidad Nacional Autonoma de Mexico, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacan 58090 (Mexico); Diaz-Polo, Jacobo [Departamento de AstronomIa y AstrofIsica, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Fernandez-Borja, Enrique [Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC. Universidad de Valencia, Burjassot-46100, Valencia (Spain)
2007-05-15
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.
Corrected entropy of BTZ black hole in tunneling approach
Modak, Sujoy Kumar
2008-01-01
We investigate further the recent analysis \\cite{R.Banerjee2}, based on a Hamilton-Jacobi type approach, to compute the temperature and entropy of black holes beyond the semiclassical approximation. It is shown how non spherically symmetric geometries are inducted in the general formalism by explicitly considering the BTZ black hole. The leading (logarithmic) and non leading corrections to the area law are obtained.
Corrected entropy of BTZ black hole in tunneling approach
Energy Technology Data Exchange (ETDEWEB)
Modak, Sujoy Kumar [S.N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata 700098 (India)], E-mail: sujoy@bose.res.in
2009-01-12
We investigate further the recent analysis [R. Banerjee, B.R. Majhi, JHEP 0806 (2008) 095, (arXiv: 0805.2220)], based on a Hamilton-Jacobi type approach, to compute the temperature and entropy of black holes beyond the semiclassical approximation. It is shown how nonspherically symmetric geometries are inducted in the general formalism by explicitly considering the BTZ black hole. The leading (logarithmic) and nonleading corrections to the area law are obtained.
Corrected entropy of BTZ black hole in tunneling approach
Modak, Sujoy Kumar
2009-01-01
We investigate further the recent analysis [R. Banerjee, B.R. Majhi, JHEP 0806 (2008) 095, arxiv:arXiv: 0805.2220], based on a Hamilton-Jacobi type approach, to compute the temperature and entropy of black holes beyond the semiclassical approximation. It is shown how nonspherically symmetric geometries are inducted in the general formalism by explicitly considering the BTZ black hole. The leading (logarithmic) and nonleading corrections to the area law are obtained.
BTZ Black Hole Entropy and the Turaev-Viro model
Geiller, Marc
2013-01-01
We show the explicit agreement between the derivation of the Bekenstein-Hawking entropy of a Euclidean BTZ black hole from the point of view of spin foam models and canonical quantization. This is done by considering a graph observable (corresponding to the black hole horizon) in the Turaev-Viro state sum model, and then analytically continuing the resulting partition function to negative values of the cosmological constant.
Entropy counting for microscopic black holes in LQG
Corichi, A; Fernandez-Borja, E; Corichi, Alejandro; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique
2007-01-01
Quantum black holes within the loop quantum gravity (LQG) framework are considered. The number of microscopic states that are consistent with a black hole of a given horizon area $A_0$ are computed and the statistical entropy, as a function of the area, is obtained for $A_0$ up to $550 l^2_P$. The results are consistent with an asymptotic linear relation and a logarithmic correction with a coefficient equal to -1/2. The Barbero-Immirzi parameter that yields the asymptotic linear relation compatible with the Bekenstein-Hawking entropy is shown to coincide with a value close to $\\gamma=0.274$, which has been previously obtained analytically. However, a new and unexpected functional form for the entropy is found for small, Planck size, black holes that calls for a physical interpretation.
Statistical Entropy of Horowitz—Strominger Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAORen; ZHANGJun－Fang; 等
2002-01-01
The partition functions of bosonic and fermionic fields in Horowitz-Strominger black hole are derived directly by quantum statistical method.Then via the improved brick-wall method (membrane model),the statistical entropy of black hole is obtained.If a proper parameter is chosen in our result,it is found out that the entropy is proportional to the area of horizon.The stripped term and the divergent logarithmic term in the original brick-wall method no longer exist.The difficulty in solving the wave equations of scalar and Dirac fields is avoided.A new neat way of calculating the entropy of various complicated black holes is offered.
Entropy of Three-Charge Black Holes on a Circle
Harmark, Troels; Obers, Niels A; Ronne, Peter B; 10.1002/prop.200610359
2007-01-01
We study phases of five-dimensional three-charge black holes with a circle in their transverse space. In particular, when the black hole is localized on the circle we compute the corrections to the metric and corresponding thermodynamics in the limit of small mass. When taking the near-extremal limit, this gives the corrections to the finite entropy of the extremal three-charge black hole as a function of the energy above extremality. For the partial extremal limit with two charges sent to infinity and one finite we show that the first correction to the entropy is in agreement with the microscopic entropy by taking into account that the number of branes shift as a consequence of the interactions across the transverse circle.
Time Evolution of Entanglement Entropy from Black Hole Interiors
Hartman, Thomas
2013-01-01
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
Time evolution of entanglement entropy from black hole interiors
Hartman, Thomas; Maldacena, Juan
2013-05-01
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
Entropy calculation for a toy black hole
Energy Technology Data Exchange (ETDEWEB)
Sahlmann, Hanno [Spinoza Institute and ITP, Utrecht University, Utrecht (Netherlands)
2008-03-07
In this paper, we carry out the counting of states for a black hole in loop quantum gravity, assuming however an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a nice and simplifying 'laboratory' for questions about the full theory.
Extremal Black Hole Entropy from Horizon Conformal Field Theories
Halyo, Edi
2015-01-01
We show that the entropy of extremal $D=4$ Reissner--Nordstrom black holes can be computed from horizon CFTs with central charges and conformal weights fixed by the dimensionless Rindler energy. This is possible in the simultaneous extremal and near horizon limit of the black hole which takes the geometry to an $AdS_2$ Rindler space with finite temperature. The CFT description of dilatonic $AdS_2$ black holes, obtained from extremal ones by dimensional reduction, lead to exactly the same CFT states.
Quantum-corrected finite entropy of noncommutative acoustic black holes
Anacleto, M. A.; Brito, F. A.; Luna, G. C.; Passos, E.; Spinelly, J.
2015-11-01
In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2 + 1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.
Black hole entropy from non-perturbative gauge theory
Kabat, D; Lowe, D A; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2001-01-01
We present the details of a mean-field approximation scheme for the quantum mechanics of N D0-branes at finite temperature. The approximation can be applied at strong 't Hooft coupling. We find that the resulting entropy is in good agreement with the Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with 0-brane charge. This result is in accord with the duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. We discuss ways of resolving the black hole horizon, and also study the spectrum of single-string excitations within the quantum mechanics.
On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry
Corichi, A
2003-01-01
Loop quantum gravity can account for the Bekenstein-Hawking entropy of a black hole provided a free parameter is chosen appropriately. Recently it was proposed that a new choice of parameter could predict both black hole entropy and the frequencies of quasinormal modes in the large $n$ limit, but at the price of changing the gauge group of the theory. In this note we use a simple physical argument to support SU(2) as the relevant gauge group. The argument uses strongly the necessity of having fermions satisfying basic conservation principles.
Quantum-corrected finite entropy of noncommutative acoustic black holes
Anacleto, M A; Luna, G C; Passos, E; Spinelly, J
2015-01-01
In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.
Black Hole Entropy Calculation in a Modified Thin Film Model
Indian Academy of Sciences (India)
Jingyi Zhang
2011-03-01
The thin film model is modified to calculate the black hole entropy. The difference from the original method is that the Parikh–Wilczek tunnelling framework is introduced and the self-gravitation of the emission particles is taken into account. In terms of our improvement, if the entropy is still proportional to the area, then the emission energy of the particles will satisfy = /360.
CFT and Logarithmic Corrections of Black Hole Entropy Product Formula
Pradhan, Parthapratim
2016-01-01
We examine the \\emph{effects of CFT} (conformal field theory) on the logarithmic corrections of black hole (BH) entropy product formula of outer horizon and inner horizon by explicitly giving several examples. We also argue that logarithmic corrections of BH entropy product formula when calculated via CFT the formula also should \\emph{not be universal} and it also should \\emph{not be quantized}.
Quantum Black Hole Entropy and Localization in Supergravity
Reys, Valentin
2016-01-01
In this thesis, we examine in detail the notion of black hole entropy in Quantum Field Theories, with a specific focus on supersymmetric black holes and the perturbative and non-perturbative quantum corrections to the classical area-law of Bekenstein-Hawking. To examine such corrections, we employ the formalism of Sen's Quantum Entropy Function where the complete quantum entropy of a supersymmetric black hole in theories of supergravity is defined as a path-integral in the near-horizon region of the black hole. Evaluation of this path-integral can then be conducted exactly using localization computation techniques. Due to the exactness of the localization argument, the results obtained in this manner are therefore formally expected to re-sum all perturbative and non-perturbative corrections to the classical area-law, and thus connect to string-theoretic predictions. We investigate such connections in detail for specific supersymmetric black holes in the hopes of strengthening a Boltzmann-type interpretation o...
Scalar field entanglement entropy for small Schwarzschild black hole
Teslyk, Maksym; Teslyk, Olena
2013-01-01
We consider scalar field entanglement entropy generated with black hole of (sub)planck mass scale thus implying the unitary evolution of gravity. The dependence on the dimension of the Hilbert space for degrees of freedom located behind the horizon is taken into account. The obtained results contain polylogarithmic terms.
Black hole entropy from loop quantum gravity in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Bodendorfer, N., E-mail: norbert@gravity.psu.edu
2013-11-04
We propose a derivation for computing black hole entropy for spherical non-rotating isolated horizons from loop quantum gravity in four and higher dimensions. The state counting problem effectively reduces to the well studied 3+1-dimensional one based on an SU(2)-Chern–Simons theory, differing only in the precise form of the area spectrum.
Logarithmic corrections in black hole entropy product formula
Pradhan, Parthapratim
2016-07-01
It has been shown by explicit and exact calculation that whenever we have taken the effects of stable thermal fluctuations, the entropy product formula should not be mass-independent nor does it quantized. It has been examined by giving some specific examples for non-rotating and rotating black hole.
Simple regular black hole with logarithmic entropy correction
Morales--Durán, Nicolás; Hoyos--Restrepo, Paulina; Bargueño, Pedro
2016-01-01
A simple regular black hole solution satisfying the weak energy condition is obtained within Einstein--non--linear electrodynamics theory. We have computed the thermodynamic properties of this black hole by a careful analysis of the horizons and we have found that the usual Bekenstein--Hawking entropy gets corrected by a logarithmic term. Therefore, in this sense our model realizes some quantum gravity predictions which add this kind of correction to the black hole entropy. In particular, we have established some similitudes between our model and a quadratic generalized uncertainty principle. This similitude has been confirmed by the existence of a remnant, which prevents complete evaporation, in agreement with the quadratic generalized uncertainty principle case.
Quantum Statistical Entropy of Spherical Black Holes in Higher Dimensions
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2000-01-01
The free energy and entropy of a general spherically symmetry black hole are calculated by quantum statistic method with brick wall model Two different kinds of approximation are used to calculate the number of states in transverse spatial space. The final results are approximately equal except a rational numerical constant. The formulas of free energy and entropy, evaluated by each one of the two different kinds of approximation, are the same except some numerical constants. The free energy and entropy are dependent on the spacetime dimensionsD. When D = 4, they reduce to the usual well known results.
Black hole entropy: lessons from loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Barbero G, J Fernando, E-mail: fbarbero@iem.cfmac.csic.es [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain)
2011-09-22
The purpose of this contribution is is to discuss black hole entropy in the loop quantum gravity framework. Special attention is paid to the description of the microscopic degrees of freedom responsible for the entropy, the statement of the combinatorial problems that must be solved in order to count them, and the behaviour of the entropy as a function of the horizon area. In particular I will review the derivation of the Bekenstein-Hawking law and its logarithmic corrections. I end with a comparison between the results derived within loop quantum gravity and the ones obtained by other approaches.
Extremal non-BPS black holes and entropy extremization
Lópes-Cardoso, G; Lust, D; Perz, J; Cardoso, Gabriel Lopes; Grass, Viviane; Lust, Dieter; Perz, Jan
2006-01-01
At the horizon, a static extremal black hole solution in N=2 supergravity in four dimensions is determined by a set of so-called attractor equations which, in the absence of higher-curvature interactions, can be derived as extremization conditions for the black hole potential or, equivalently, for the entropy function. We contrast both methods by explicitly solving the attractor equations for a one-modulus prepotential associated with the conifold. We find that near the conifold point, the non-supersymmetric solution has a substantially different behavior than the supersymmetric solution. We analyze the stability of the solutions and the extrema of the resulting entropy as a function of the modulus. For the non-BPS solution the region of attractivity and the maximum of the entropy do not coincide with the conifold point.
A note on black hole entropy in loop quantum gravity
Carlip, S.
2015-08-01
Several recent results have hinted that black hole thermodynamics in loop quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi parameter γ =i. This suggests a connection with {SL}(2,{{C}}) or {SL}(2,{{R}}) conformal field theories at the ‘boundaries’ formed by spin network edges intersecting the horizon. I present a bit of background regarding the relevant conformal field theories, along with some speculations about how they might be used to count black hole states. I show, in particular, that a set of unproven but plausible assumptions can lead to a boundary conformal field theory whose density of states matches the Bekenstein-Hawking entropy.
Universal near-horizon conformal structure and black hole entropy
Chakrabarti, Sayan K; Sen, Siddhartha
2007-01-01
It is shown that a massless scalar probe reveals a universal near-horizon conformal structure for a wide class of black holes, including the BTZ. The central charge of the corresponding Virasoro algebra contains information about the black hole. With a suitable quantization condition on the central charge, the CFT associated with the black hole in our approach is consistent with the recent observation of Witten, where the dual theory for the BTZ in the AdS/CFT framework has been identified with the construction of Frenkel, Lepowsky and Meurman. This CFT admits the Fischer-Griess monster group as its symmetry. The logarithm of the dimension of a specific representation of the monster group has been identified by Witten as the entropy of the BTZ black hole. Our algebraic approach shows that a wide class of black holes share the same near-horizon conformal structure as that for the BTZ. With a suitable quantization condition, the CFT's for all these black holes can be identified with the FLM model and the corres...
A note on entropy of de Sitter black holes
Bhattacharya, Sourav
2015-01-01
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons -- a black hole horizon and a cosmological event horizon surrounding it. It is natural to expect that the total Bekenstein-Hawking entropy of such spacetimes should be the sum of the two horizons' areas. In this work we apply the recently developed formalism using the Gibbons-Hawking-York boundary term and the near horizon symmetries to derive the total entropy of such two horizon spacetimes. We first use a suitable general geometric set up for stationary axisymmetric spacetimes with two or more than two commuting Killing vector fields in an arbitrary spacetime dimensions. This framework helps us to deal with both the horizons in an equal footing and to obtain the total entropy. We show that in order get the total entropy, the near horizon mode functions for the diffeomorphism generating vector fields has to be restricted in a certain manner, compared to the single horizon spacetimes. We nex...
Black hole entropy, topological entropy and the Baum-Connes conjecture in K-theory
International Nuclear Information System (INIS)
We shall try to show a relation between black hole (BH) entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for BHs, provided by superstring theory, in the more general noncommutative geometric context of M-theory following the approach of Connes-Douglas-Schwarz. (author)
Black hole entropy, topological entropy and the Baum-Connes conjecture in K-theory
Energy Technology Data Exchange (ETDEWEB)
Zois, Ioannis P. [Mathematical Institute, Oxford University, Oxford (United Kingdom)]. E-mail: izois@maths.ox.ac.uk
2002-03-29
We shall try to show a relation between black hole (BH) entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for BHs, provided by superstring theory, in the more general noncommutative geometric context of M-theory following the approach of Connes-Douglas-Schwarz. (author)
Entropy localization and extensivity in the semiclassical black hole evaporation
International Nuclear Information System (INIS)
I aim to quantify the distribution of information in the Hawking radiation and inside the black hole in the semiclassical evaporation process. The structure of relativistic quantum field theory does not allow one to define a localized entropy unambiguously, but rather forces one to consider the shared information (mutual information) between two different regions of space-time. Using this tool, I first show that the entropy of a thermal gas at the Unruh temperature underestimates the actual amount of (shared) information present in a region of the Rindler space. Then, I analyze the mutual information between the black hole and the late time radiation region. A well-known property of the entropy implies that this is monotonically increasing with time. This means that in the semiclassical picture it is not possible to recover the eventual purity of the initial state in the final Hawking radiation through subtle correlations established during the whole evaporation period, no matter the interactions present in the theory. I find extensivity of the entropy as a consequence of a reduction to a two dimensional conformal problem in a simple approximation. However, the extensivity of information in the radiation region in a full four dimensional calculation seems not to be guaranteed on general grounds. I also analyze the localization of shared information inside the black hole finding that a large amount of it is contained in a small, approximately flat region of space-time near the point where the horizon begins. This gives place to large violations of the entropy bounds. I show that this problem is not eased by backscattering effects and argue that a breaking of conformal invariance is necessary to delocalize the entropy. Finally, I indicate that the mutual information could lead to a way to understand the Bekenstein-Hawking black hole entropy which does not require a drastic reduction in degrees of freedom in order to regulate the entanglement entropy. On the contrary
Cosmological Entropy and Black Holes in Galactic Halos
Frampton, Paul H
2009-01-01
In this talk we discuss intermediate mass black holes (IMBHs) by their amplilification of distant sources; MACHO searches have studied event times $2 h \\lesssim t_0 \\lesssim 2 y$ corresponding masses in the range $10^{-6} M_{\\odot} \\lesssim M \\lesssim 100 M_{\\odot}$. We suggest that larger masses up to $10^6 M_{\\odot}$ are also of considerable interest by arguments about the entropy of the universe. One percent by mass of dark energy can provide ninety-nine percent of total entropy.
Increase of black hole entropy in higher curvature gravity
Jacobson, T; Myers, R C; Jacobson, Ted; Kang, Gungwon; Myers, Robert C
1995-01-01
We examine the Zeroth Law and the Second Law of black hole thermodynamics within the context of effective gravitational actions including higher curvature interactions. We show that entropy can never decrease for quasi-stationary processes in which a black hole accretes positive energy matter, independent of the details of the gravitational action. Within a class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar, we use a conformally equivalent theory to establish that stationary black hole solutions with a Killing horizon satisfy the Zeroth Law, and that the Second Law holds in general for any dynamical process. We also introduce a new method for establishing the Second Law based on a generalization of the area theorem, which may prove useful for a wider class of Lagrangians. Finally, we show how one can infer the form of the black hole entropy, at least for the Ricci polynomial theories, by integrating the changes of mass and angular momentum in a quasistationary...
Loop quantum gravity in higher dimensions and black hole entropy
International Nuclear Information System (INIS)
A reformulation of higher-dimensional gravity theories is discussed which allows for the application of the loop quantum gravity program. To this end, a Hamiltonian formulation of the gravity theory has to be given on a Yang-Mills phase space such that the Yang-Mills gauge group is compact, the Poisson brackets are canonical, the variables are real and the theory is only subject to first class constraints. The computation of black hole entropy is discussed as an application.
Bound of Noncommutativity Parameter Based on Black Hole Entropy
Kim, Wontae; Lee, Daeho
2010-01-01
We study the bound of the noncommutativity parameter in the noncommutative Schwarzschild black hole which is a solution of the noncommutative ISO(3,1) Poincare gauge group. The statistical entropy satisfying the area law in the brick wall method yields a cutoff relation which depends on the noncommutativity parameter. Requiring both the cutoff parameter and the noncommutativity parameter to be real, the noncommutativity parameter can be shown to be bounded as $\\Theta > 8.4\\ times 10^{-2}l_{p}$.
Loop quantum gravity in higher dimensions and black hole entropy
Energy Technology Data Exchange (ETDEWEB)
Bodendorfer, Norbert [IFT UW, Warschau (Poland)
2014-07-01
A reformulation of higher-dimensional gravity theories is discussed which allows for the application of the loop quantum gravity program. To this end, a Hamiltonian formulation of the gravity theory has to be given on a Yang-Mills phase space such that the Yang-Mills gauge group is compact, the Poisson brackets are canonical, the variables are real and the theory is only subject to first class constraints. The computation of black hole entropy is discussed as an application.
A note on entropy of de Sitter black holes
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Sourav [University of Crete, ITCP and Department of Physics, Heraklion (Greece); Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune (India)
2016-03-15
A de Sitter black hole or a black hole spacetime endowed with a positive cosmological constant has two Killing horizons - a black hole and a cosmological event horizon surrounding it. It is natural to expect that the total Bekenstein-Hawking entropy of such spacetimes should be the sum of the two horizons' areas. In this work we apply the recently developed formalism using the Gibbons-Hawking-York boundary term and the near horizon symmetries to derive the total entropy of such two horizon spacetimes. We construct a suitable general geometric set up for general stationary axisymmetric spacetimes with two or more than two commuting Killing vector fields in an arbitrary spacetime dimensions. This framework helps us to deal with both horizons on an equal footing. We show that in order to obtain the total entropy of such spacetimes, the near horizon mode functions for the diffeomorphism generating vector fields have to be restricted in a certain manner, compared to the single horizon spacetimes. We next discuss specific known exact solutions belonging to the Kerr-Newman or the Plebanski-Demianski-de Sitter families to show that they fall into the category of our general framework. We end with a sketch of further possible extensions of this work. (orig.)
Black-hole entropy and minimal diffusion
Arzano, Michele; Calcagni, Gianluca
2013-01-01
The density of states reproducing the Bekenstein-Hawking entropy-area scaling can be modeled via a nonlocal field theory. We define a diffusion process based on the kinematics of this theory and find a spectral dimension whose flow exhibits surprising properties. While it asymptotes four from above in the infrared, in the ultraviolet the spectral dimension diverges at a finite (Planckian) value of the diffusion length, signaling a breakdown of the notion of diffusion on a continuum spacetime ...
A discussion of a possible corrected black hole entropy
He, Miao; Fang, Chao; Sun, Dao-Quan; Deng, Jian-Bo
2016-01-01
Einstein's equation could be interpreted as the first law of thermodynamic near the spherically symmetric horizon. By using this method, we investigate the Eddington-inspired Born-Infeld (EiBI) gravity. Without matter field, the EiBI gravity can also derive the first law. With an electromagnetic field, as the field equations have a more general spherically symmetric solution in EiBI gravity, we find that the entropy would have a correction. Through recalling the Einstein gravity with a more general static spherical symmetric, this correction of the entropy might be generalized to Einstein gravity. Furthermore, we point out that the Einstein gravity and EiBI gravity might be equivalent on the event horizon. At last, under EiBI gravity with the electromagnetic field, a specific corrected entropy of black hole is given.
Area and entropy spectra of black holes via an adiabatic invariant
Institute of Scientific and Technical Information of China (English)
Liu Cheng-Zhou
2012-01-01
By considering and using an adiabatic invariant for black holes,the area and entropy spectra of static sphericallysymmetric black holes are investigated.Without using quasi-normal modes of black holes,equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant.The spectra for non-charged and charged black holes are calculated,respectively.All these results are consistent with the original Bekenstein spectra.
Entropy of localized states and black hole evaporation
International Nuclear Information System (INIS)
We call a state 'vacuum bounded' if every measurement performed outside a specified interior region gives the same result as in the vacuum. We compute the maximum entropy of a vacuum-bounded state with a given energy for a one-dimensional model, with the aid of numerical calculations on a lattice. The maximum entropy is larger than it would be for rigid wall boundary conditions by an amount δS, which for large energies is approx-lt(1)/(6)ln(LinT), where Lin is the length of the interior region. Assuming that the state resulting from the evaporation of a black hole is similar to a vacuum-bounded state, and that the similarity between vacuum-bounded and rigid-wall-bounded problems extends from 1 to 3 dimensions, we apply these results to the black hole information paradox. Under these assumptions we conclude that large amounts of information cannot be emitted in the final explosion of a black hole. copyright 1997 The American Physical Society
Entropy of the information retrieved from black holes
Mersini-Houghton, Laura
2016-07-01
The retrieval of black hole information was recently presented in two interesting proposals in the ‘Hawking Radiation’ conference: a revised version by Hooft of a proposal he initially suggested 20 years ago and, a new proposal by Hawking. Both proposals address the problem of black hole information loss at the classical level and derive an expression for the scattering matrix. The former uses gravitation back reaction of incoming particles that imprints its information on the outgoing modes. The latter uses supertranslation symmetry of horizons to relate a phase delay of the outgoing wave packet compared to their incoming wave partners. The difficulty in both proposals is that the entropy obtained from them appears to be infinite. By including quantum effects into the Hawking and Hooft’s proposals, I show that a subtlety arising from the inescapable measurement process, the quantum Zeno effect, not only tames divergences but it actually recovers the correct 1/4 of the area Bekenstein-Hawking entropy law of black holes.
Logarithmic Black Hole Entropy Corrections and Holographic R\\'enyi Entropy
Mahapatra, Subhash
2016-01-01
The entanglement and R\\'{e}nyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of horizon area. With the corrected black hole entropy expression, we then find corrections to the R\\'{e}nyi entropies. We calculate these corrections for both Einstein as well as Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order $G_{D}^0$ and it seems to be a general feature of entanglement and R\\'{e}nyi entropies for CFTs with gravity duals. In particular, there is...
Einstein Prize: Black Hole Entropy - Then and Now
Bekenstein, Jacob
2015-04-01
Forty five year ago black holes were universally regarded as gravitational entities with only mechanical and electrical attributes. There then occurred a shift in thinking and we became accustomed to regard those exotic objects as also subject to thermodynamics. I shall recollect the forerunners of this conceptual change e.g. Hawking's black hole area increase theorem, and some of the steps by which it took place. The transition involved the introduction of black hole entropy and temperature, and the formulation of a generalized version of the second law. This last proved prophetic with the discovery of Hawking's radiance, a phenomenon which transcends the area increase theorem, but upholds the generalized second law. The thermodynamic paradigm for black holes has brought us face to face with subtle issues having to to do with the significance of information in physics, and the seeming collision between gravitational theory and quantum mechanics. Among the concrete fruits of the new way of thinking are various results on the peak information capacity of physical systems, as well as the ``holographic'' approach by which intricate calculations in quantum field theory (with applications to elementary particles or condensed matter physics) can be traded for tractable ones in classical gravity theory.
Bosonic and Fermionic Entropy of (2+1)-Dimensional Charged Black Hole
Institute of Scientific and Technical Information of China (English)
CHEN Ju-Hua; WANG Yong-Jiu; JING Ji-Liang
2001-01-01
From resolving Klein-Gordon equation and Dirac equation in (2+1)-dimensional charged black hole spacetime and using 't Hooft's boundary condition and "quasi-periodic" boundary condition in the thin film brick wall model of black hole, which is introduced by LIU Weng-Biao and ZHAO Zheng, we obtain the bosonic and fermionic entropy of (2+1)-dimensional charged black hole, and find that the bosonic entropy is three times of fermionic entropy.
Entropy Spectrum of Modified Schwarzschild Black Hole via an Action Invariance
Indian Academy of Sciences (India)
Cheng-Zhou Liu
2014-09-01
The entropy spectrum of a modified Schwarzschild black hole in the gravity’s rainbow are investigated. By utilizing an action invariance of the black hole with the help of Bohr–Sommerfield quantization rule, the entropy spectrum for the modified black hole are calculated. The result of the equally spaced-entropy spectrum being consistent to the original Bekenstein’s spectra is derived.
Entropy of Non-Extremal Black Holes from Loop Gravity
Bianchi, Eugenio
2012-01-01
We compute the entropy of non-extremal black holes using the quantum dynamics of Loop Gravity. The horizon entropy is finite, scales linearly with the area A, and reproduces the Bekenstein-Hawking expression S = A/4 with the one-fourth coefficient for all values of the Immirzi parameter. The near-horizon geometry of a non-extremal black hole - as seen by a stationary observer - is described by a Rindler horizon. We introduce the notion of a quantum Rindler horizon in the framework of Loop Gravity. The system is described by a quantum surface and the dynamics is generated by the boost Hamiltonion of Lorentzian Spinfoams. We show that the expectation value of the boost Hamiltonian reproduces the local horizon energy of Frodden, Ghosh and Perez. We study the coupling of the geometry of the quantum horizon to a two-level system and show that it thermalizes to the local Unruh temperature. The derived values of the energy and the temperature allow one to compute the thermodynamic entropy of the quantum horizon. The...
Black Hole Entropy Associated with Supersymmetric Sigma Model
Abdalla, Maria Christina B; Guimarães, M E X
2003-01-01
By means of an identity that equates elliptic genus partition function of a supersymmetric sigma model on the $N$-fold symmetric product $S^N X$ of $X$ ($S^N X=X^N/S_N$, $S_N$ is the symmetric group of $N$ elements) to the partition function of a second quantized string theory, we derive the asymptotic expansion of the partition function as well as the asymptotic for the degeneracy of spectrum in string theory. The asymptotic expansion for the state counting reproduces the logarithmic correction to the black hole entropy.
Entropy of Black Holes: A Quantum Algebraic Approach
Directory of Open Access Journals (Sweden)
G. Vitiello
2003-02-01
Full Text Available Abstract: In this paper we apply to a class of static and time-independent geometries the recently developed formalism of deformed algebras of quantum fields in curved backgrounds. In particular we derive: i some non-trivial features of the entanglement of the quantum vacuum, such as the robustness against interaction with the environment; ii the thermal properties and the entropy of black holes for space-times with a unique event horizon, such as Schwarzschild, de Sitter and Rindler space-times.
Modification of black-hole entropy by strings
Parthasarathy, R
1996-01-01
A generalized action for strings which is a sum of the Nambu-Goto and the extrinsic curvature (the energy integral of the surface) terms, is used to couple strings to gravity. It is shown that the conical singularity has deficit angle that has contributions from both the above terms. It is found that the effect of extrinsic curvature is to oppose that of the N-G action for the temperature of the black-hole and to modify the entropy-area relation.
Dyonic AdS_4 black hole entropy and attractors via entropy function
Goulart, Prieslei
2015-01-01
Using the Sen's entropy function formalism, we compute the entropy for the extremal dyonic black hole solutions of theories in the presence of dilaton field coupled to the field strength and a dilaton potential. We solve the attractor equations analytically and determine the near horizon metric, the value of the scalar fields and the electric field on the horizon, and consequently the entropy of these black holes. The attractor mechanism plays a very important role for these systems, and after studying the simplest systems involving dilaton fields, we propose a general ansatz for the value of the scalar field on the horizon, which allows us to solve the attractor equations for gauged supergravity theories in AdS_4 spaces.
Statistical Entropy of the Kaluza－Klein Black Hole from the Horizon Conformal Field Theory
Institute of Scientific and Technical Information of China (English)
JING Ji-Liang; YAN Mu-Lin
2001-01-01
The statistical entropy of the Kaluza-Klein black hole is studied by counting the black hole states which form an algebra of diffeomorphism at Killing horizon with a central charge. It is shown that the entropy yielded by the standard Cardy formula agrees with the Bekenstein-Hawking entropy only if we take period T of function u as the periodicity of the Euclidean black hole. On the other hand, the first-order quantum correction to the entropy is proportional to the logarithm of the Bekenstein-Hawking entropy with a factor -1/2.
Analytic continuation of black hole entropy in Loop Quantum Gravity
Jibril, Ben Achour; Mouchet, Amaury; Noui, Karim
2015-06-01
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter γ. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined à la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature T U associated to this local observer. When γ = ± i, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value μ = 2 T U.
Statistics, holography, and black hole entropy in loop quantum gravity
Ghosh, Amit; Noui, Karim; Perez, Alejandro
2014-04-01
In loop quantum gravity the quantum states of a black hole horizon consist of pointlike discrete quantum geometry excitations (or punctures) labeled by spin j. The excitations possibly carry other internal degrees of freedom, and the associated quantum states are eigenstates of the area A operator. The appropriately scaled area operator A/(8πℓ) can also be interpreted as the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance ℓ from the horizon. Thus, the local energy is entirely accounted for by the geometric operator A. Assuming that: Close to the horizon the quantum state has a regular energy momentum tensor and hence the local temperature measured by stationary observers is the Unruh temperature. Degeneracy of matter states is exponential with the area exp(λA/ℓp2), which is supported by the well-established results of QFT in curved spacetimes, which do not determine λ but assert an exponential behavior. The geometric excitations of the horizon (punctures) are indistinguishable. And finally that the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound, viz., λ must be equal to 1/4. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy S =A/(4ℓp2). The number of horizon punctures goes like N∝√A/ℓp2 ; i.e., the number of punctures N remains large in the semiclassical limit. Fluctuations of the horizon area are small ΔA/A ∝(ℓp2/A)1/4, while fluctuations of the area of an individual puncture are large (large spins dominate). A precise notion of local conformal invariance of the thermal state is recovered in the A→∞ limit where the near horizon geometry becomes Rindler. We also show how the present model (constructed from loop quantum gravity) provides a regularization of (and gives a concrete meaning to) the formal
Do gauge fields really contribute negatively to black hole entropy?
Donnelly, William
2012-01-01
Quantum fluctuations of matter fields contribute to the thermal entropy of black holes. For free minimally-coupled scalar and spinor fields, this contribution is precisely the entanglement entropy. For gauge fields, Kabat found an extra negative divergent "contact term" with no known statistical interpretation. We compare this contact term to a similar term that arises for nonminimally-coupled scalar fields. Although both divergences may be interpreted as terms in the Wald entropy, we point out that the contact term for gauge fields comes from a gauge-dependent ambiguity in Wald's formula. Revisiting Kabat's derivation of the contact term, we show that it is sensitive to the treatment of infrared modes. To explore these infrared issues, we consider two-dimensional compact manifolds, such as Euclidean de Sitter space, and show that the contact term arises from an incorrect treatment of zero modes. In a manifestly gauge-invariant reduced phase space quantization, the gauge field contribution to the entropy is p...
Isolated Horizons and Black Hole Entropy in Loop Quantum Gravity
Directory of Open Access Journals (Sweden)
Jacobo Diaz-Polo
2012-08-01
Full Text Available We review the black hole entropy calculation in the framework of Loop Quantum Gravity based on the quasi-local definition of a black hole encoded in the isolated horizon formalism. We show, by means of the covariant phase space framework, the appearance in the conserved symplectic structure of a boundary term corresponding to a Chern-Simons theory on the horizon and present its quantization both in the U(1 gauge fixed version and in the fully SU(2 invariant one. We then describe the boundary degrees of freedom counting techniques developed for an infinite value of the Chern-Simons level case and, less rigorously, for the case of a finite value. This allows us to perform a comparison between the U(1 and SU(2 approaches and provide a state of the art analysis of their common features and different implications for the entropy calculations. In particular, we comment on different points of view regarding the nature of the horizon degrees of freedom and the role played by the Barbero-Immirzi parameter. We conclude by presenting some of the most recent results concerning possible observational tests for theory.
Thermodynamics of BTZ black hole and entanglement entropy
International Nuclear Information System (INIS)
The BTZ black Hole is (2+1) dimensional black hole solution asymptotic to anti-de-Sitter space-time. We study the discretized quantum scalar fields in background of non-rotating BTZ black hole space-time and construct the entanglement thermodynamics for massless scalar field. The behavior of the entanglement energy is understood by red shift factor caused by the curved background. The entanglement thermodynamics is compared with the black hole thermodynamics
Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP
Anacleto, M. A.; Brito, F. A.; Passos, E.
2015-10-01
In this paper we focus on the Hamilton-Jacobi method to determine the entropy of a self-dual black hole by using linear and quadratic GUPs (generalized uncertainty principles). We have obtained the Bekenstein-Hawking entropy of self-dual black holes and its quantum corrections that are logarithm and also of several other types.
Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP
Directory of Open Access Journals (Sweden)
M.A. Anacleto
2015-10-01
Full Text Available In this paper we focus on the Hamilton–Jacobi method to determine the entropy of a self-dual black hole by using linear and quadratic GUPs (generalized uncertainty principles. We have obtained the Bekenstein–Hawking entropy of self-dual black holes and its quantum corrections that are logarithm and also of several other types.
Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP
Anacleto, M A; Passos, E
2015-01-01
In this paper we focus on the Hamilton-Jacobi method to determine the entropy of a self-dual black hole by using linear and quadratic GUPs(generalized uncertainty principles). We have obtained the Bekenstein-Hawking entropy of self-dual black holes and its quantum corrections that are logarithm and also of several other types.
Statistical Entropy of Nonextremal Four-Dimensional Black Holes and U-Duality
International Nuclear Information System (INIS)
We identify the states in string theory which are responsible for the entropy of near-extremal rotating four-dimensional black holes in N=8 supergravity. For black holes far from extremality (with no rotation), the Bekenstein-Hawking entropy is exactly matched by a mysterious duality invariant extension of the formulas derived for near-extremal black holes states. copyright 1996 The American Physical Society
Entropy in the NUT-Kerr-Newman Black Holes in the Background of de Sitter Spacetime
Institute of Scientific and Technical Information of China (English)
葛先辉; 沈有根
2002-01-01
We calculate the entropy of the fermion field in the NUT-Kerr-Newman black holes in the background of the de Sitter spacetime by using the improved brick-wall method and the membrane model. Here the Euler characteristic of the black holes is over two. The results show that, as the cut-off is properly chosen, the entropy in the black hole satisfies the Bekenstein-Hawking area law.
Topological Aspects of Entropy and Phase Transition of Kerr Black Holes
Institute of Scientific and Technical Information of China (English)
YANG Guo-Hong; YAN Ji-Jiang; TIAN Li-Jun; DUAN Yi-Shi
2005-01-01
In the light of topological current and the relationship between the entropy and the Euler characteristic, the topological aspects of entropy and phase transition of Kerr black holes are studied. From Gauss-Bonnet-Chern theorem,it is shown that the entropy of Kerr black holes is determined by the singularities of the Killing vector field of spacetime.By calculating the Hopf indices and Brouwer degrees of the Killing vector field at the singularities, the entropy S = A/4for nonextreme Kerr black holes and S = 0 for extreme ones are obtained, respectively. It is also discussed that, with the change of the ratio of mass to angular momentum for unit mass, the Euler characteristic and the entropy of Kerr black holes will change discontinuously when the singularities on Cauchy horizon merge with the singularities on event horizon, which will lead to the first-order phase transition of Kerr black holes.
On the Entropy Function and the Attractor Mechanism for Spherically Symmetric Extremal Black Holes
Cai, Rong-Gen; Cao, Li-Ming
2007-01-01
In this paper we elaborate on the relation between the entropy formula of Wald and the "entropy function" method proposed by A. Sen. For spherically symmetric extremal black holes, it is shown that the expression of extremal black hole entropy given by A. Sen can be derived from the general entropy definition of Wald, without help of the treatment of rescaling the AdS_2 part of near horizon geometry of extremal black holes. In our procedure, we only require that the surface gravity approaches...
Tawfik, Abdel Nasser
2015-01-01
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes; Schwarzschild, Garfinkle-Horowitz-Strominger and Reissner-Nordstr\\"om is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be positive. The entropy $S$, which is assumed to be related to horizon's two-dimensional area, gets an additional terms, for instance $2\\, \\sqrt{\\pi}\\, \\alpha\\, \\sqrt{S}$, where $\\alpha$ is the GUP parameter.
Black hole entropy and SU(2) Chern-Simons theory.
Engle, Jonathan; Noui, Karim; Perez, Alejandro
2010-07-16
Black holes (BH's) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area a(H), the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to a(H) with logarithmic corrections ΔS=-3/2 loga(H). Our treatment from first principles settles previous controversies concerning the counting of states. PMID:20867755
Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Li-Chun
2003-01-01
In this paper, by using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the 5-dimensional rotating black hole. Then via the improved brick-wall method and membrane model, we calculate the entropy of Bose field and Fermi field of the black hole. And it is obtained that the entropy of the black hole is not only related to the area of the outer horizon but also is the function of inner horizon's area. In our results, there are not the left out term and the divergent logarithmic term in the original brick-wall method.The doubt that why the entropy of the scalar or Dirac field outside the event horizon is the entropy of the black hole in the original brick-wall method does not exist. The influence of spinning degeneracy of particles on entropy of the black hole is also given. It is shown that the entropy determined by the areas of the inner and outer horizons will approach zero,when the radiation temperature of the black hole approaches absolute zero. It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy. We provide a way to study higher dimensional black hole.
Entropy of the Information Retrieved from Black Holes
Mersini-Houghton, Laura
2015-01-01
The retrieval of black hole information was recently presented in two interesting proposals in the 'Hawking Radiation' conference: a revised version by G. 't Hooft of a proposal he initially suggested 20 years ago and, a new proposal by S. Hawking. Both proposals address the problem of black hole information loss at the classical level and derive an expression for the scattering matrix. The former uses gravitation back reaction of incoming particles that imprints its information on the outgoing modes. The latter uses supertranslation symmetry of horizons to relate a phase delay of the outgoing wave packet compared to their incoming wave partners. The difficulty in both proposals is that the entropy obtained from them appears to be infinite. By including quantum effects into the Hawking and 't Hooft's proposals, I show that a subtlety arising from the inescapable measurement process, the Quantum Zeno Effect, not only tames divergences but it actually recovers the correct $1/4$ of the area Bekenstein-Hawking en...
Entropy corrections to five-dimensional black holes and de Sitter spaces
Wang, Fujun; Gui, Yuanxing; Ma, Chunrui
2008-12-01
It is shown that non-rotating black holes in three or four dimensions possess a canonical entropy. Recently study indicated that there were logarithmic corrections to Bekenstein Hawking entropy in area with a uncertain coefficient which depends on specific models. In this paper, the thermal fluctuations on Bekenstein Hawking entropy in five-dimensional topological AdS (TAds)-black holes and topological de Sitter (Tds) spaces will be considered based on a uniformly spaced area spectrum approach.
Angular Momentum-Free of the Entropy Relations for Rotating Kaluza-Klein Black Holes
Liu, Hang
2016-01-01
Based on a mathematical lemma related to the Vandermonde determinant and two theorems derived from the first law of black hole thermodynamics, we investigate the angular momentum independence of the entropy sum as well as the entropy product of general rotating Kaluza-Klein black holes in higher dimensions. We show that for both non-charged rotating Kaluza-Klein black holes and non-charged rotating Kaluza-Klein-AdS black holes, the angular momentum of the black holes will not be present in entropy sum relation in dimensions $d\\geq4$, while the independence of angular momentum of the entropy product holds provided that the black holes possess at least one zero rotation parameter $a_j$ = 0 in higher dimensions $d\\geq5$, which means that the cosmological constant does not affect the angular momentum-free property of entropy sum and entropy product under the circumstances that charge $\\delta=0$. For the reason that the entropy relations of charged rotating Kaluza-Klein black holes as well as the non-charged rotat...
Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity
Kolekar, Sanved; Padmanabhan, T.; Sarkar, Sudipta
2012-07-01
We study quasistationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of the stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasistationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase theorem in a wider class of gravitational theories.
Entropy spectrum of the apparent horizon of Vaidya black holes via adiabatic invariance
Chen, Ge-Rui; Huang, Yong-Chang
2016-01-01
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 [J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)]. 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 the tunneling formalism for deriving the Hawking effect, which is interesting.
The entropy of Garfinkle-Horne dilaton black hole due to arbitrary spin fields
Institute of Scientific and Technical Information of China (English)
SHEN; Yougen(沈有根)
2002-01-01
Using the membrane model which is based on brick wall model, we calculated the free energy and entropy of Garfinkle-Horne dilatonic black hole due to arbitrary spin fields. The result shows that the entropy of scalar field and the entropy of Fermionic field have similar formulas. There is only a coefficient between them.
The Resolution of an Entropy Puzzle for 4D non-BPS Black Holes
Banerjee, Nabamita; Lodato, Ivano
2016-01-01
We show the equality between macroscopic and microscopic black hole entropy for a class of four dimensional non-supersymmetric black holes in ${\\cal N}=2$ supergravity theory, up to the first subleading order in their charges. This solves a long standing entropy puzzle for this class of black holes. The macroscopic entropy has been computed in the presence of a newly derived higher-derivative supersymmetric invariant of \\cite{{Butter:2013lta}}, connected to the five dimensional supersymmetric Weyl squared Lagrangian. Microscopically, the crucial role in obtaining the equivalence is played by the anomalous gauge gravitational Chern-Simons term.
Quasiparticle picture of black holes and the entropy--area relation
Iizuka, N; Lifschytz, G; Lowe, D A; Iizuka, Norihiro; Kabat, Daniel; Lifschytz, Gilad; Lowe, David A.
2003-01-01
We propose an effective description of 0-brane black holes, in which the black hole is modeled as a gas of non-interacting quasi-particles in the dual quantum mechanics. This simple model is shown to account for many of the static thermodynamic properties of the black hole. It also accounts for dynamical properties, such as the rate at which energy gets thermalized by the black hole. We use the model to show that the entropy of the quantum mechanics is proportional to the black hole horizon area in Planck units.
Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole
Abdolrahimi, Shohreh
2015-01-01
Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.
Four-dimensional Calabi-Yau Black holes and their entropies.
Lust, D.
The author considers extremal black hole solutions of N = 2 supergravity which arise in the context of type II superstring compactification on Calabi-Yau 3-folds. In particular he shows how the entropies of these black holes depend on the topological data of the Calabi-Yau spaces; he also constructs massless black holes which are relevant for the conifold transition among different Calabi-Yau vacua.
Fermion Fields in BTZ Black Hole Space-Time and Entanglement Entropy
International Nuclear Information System (INIS)
We study the entanglement entropy of fermion fields in BTZ black hole space-time and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. The leading term is the standard Bekenstein-Hawking area law and subleading term corresponds to first quantum corrections in black hole entropy. We also investigate the corrections to entanglement entropy for massive fermion fields in BTZ space-time. The mass term does not affect the area law
Fermion Fields in BTZ Black Hole Space-Time and Entanglement Entropy
Directory of Open Access Journals (Sweden)
Dharm Veer Singh
2015-01-01
Full Text Available We study the entanglement entropy of fermion fields in BTZ black hole space-time and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. The leading term is the standard Bekenstein-Hawking area law and subleading term corresponds to first quantum corrections in black hole entropy. We also investigate the corrections to entanglement entropy for massive fermion fields in BTZ space-time. The mass term does not affect the area law.
Computing Black Hole entropy in Loop Quantum Gravity from a Conformal Field Theory perspective
Agullo, Ivan; Diaz-Polo, Jacobo
2009-01-01
Motivated by the analogy proposed by Witten between Chern-Simons and Conformal Field Theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The consistency of the result opens a window for the interplay between Conformal Field Theory and the description of black holes in Loop Quantum Gravity.
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
Energy Technology Data Exchange (ETDEWEB)
Agulló, Iván [Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637 (United States); Borja, Enrique F. [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Díaz-Polo, Jacobo, E-mail: Ivan.Agullo@uv.es, E-mail: Enrique.Fernandez@uv.es, E-mail: Jacobo.Diaz@uv.es [Institute for Gravitation and the Cosmos, Physics Department, Penn State, University Park, PA 16802 (United States)
2009-07-01
Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity.
Liu, Hang; Meng, Xin-he
2016-08-01
In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions d > 4 with at least one rotation parameter ai = 0, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions (d > 4) and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affect the angular momentum-free of entropy sum and product but the criterion for angular momentum-independence of entropy product will be affected.
Custodio, P. S.; Horvath, J E
2003-01-01
We apply the Generalized Uncertainty Principle (GUP) to the problem of maximum entropy and evaporation/absorption of energy of black holes near the Planck scale. We find within this general approach corrections to the maximum entropy, and indications for quenching of the evaporation because not only the evaporation term goes to a finite limit, but also because absorption of quanta seems to help the balance for black holes in a thermal bath. Then, residual masses around the Planck scale may be...
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
M.A. Anacleto; Brito, F. A.; E. Passos; Santos, W. P.
2014-01-01
In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when $\\lambda$ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximati...
An Entropy Formula for Higher Spin Black Holes via Conical Singularities
Kraus, Per
2013-01-01
We consider the entropy of higher spin black holes in 2+1 dimensions using the conical singularity approach. By introducing a conical singularity along a non contractible cycle and carefully evaluating its contribution to the Chern Simons action, we derive a simple expression for the entropy of a general stationary higher spin black hole. The resulting formula is shown to satisfy the first law of thermodynamics, and yields agreement with previous results based on integrating the first law.
Energy and entropy conservation for dynamical black holes
Hayward, Sean A.
2004-01-01
The Ashtekar-Krishnan energy-balance law for dynamical horizons, expressing the increase in mass-energy of a general black hole in terms of the infalling matter and gravitational radiation, is expressed in terms of trapping horizons, allowing the inclusion of null (isolated) horizons as well as spatial (dynamical) horizons. This first law of black-hole dynamics is given in differential and integral forms, regular in the null limit. An effective gravitational-radiation energy tensor is obtaine...
Microscopic Entropy of the Magnetised Extremal Reissner-Nordstrom Black Hole
Astorino, Marco
2015-01-01
The extremal Reissner-Nordstr\\"om black hole embedded in a Melvin-like magnetic universe is studied in the framework of the Kerr/CFT correspondence. The near horizon geometry can be written as a warped and twisted product of $AdS_2 \\times S^2$, also in presence of an axial external magnetic field that deforms the black hole. The central charge of the Virasoro algebra can be extracted from the asymptotic symmetries. Using the Cardy formula for the microscopic statistical entropy of the dual two-dimensional CFT, the Bekenstein-Hawking entropy, for this charged and magnetised black hole, is reproduced.
An Improved Thin Film Brick-Wall Model of Black Hole Entropy
Institute of Scientific and Technical Information of China (English)
LIU Wen-Biao; ZHAO Zheng
2001-01-01
We improve the brick-wall model to take only the contribution of a thin film near the event horizon into account. This improvement not only gives us a satisfactory result, but also avoids some drawbacks in the original brick wall method such as the little mass approximation, neglecting logarithm term, and taking the term L3 as the contribution of the vacuum surrounding a black hole. It is found that there is an intrinsic relation between the event horizon and the entropy. The event horizon is the characteristic of a black hole, so the entropy calculating of a black hole is also naturally related to its horizon.
Entropy of quantum field in toroidal black hole without brick wall
Institute of Scientific and Technical Information of China (English)
Wang Bo-Bo
2008-01-01
In this paper the entropy of a toroidal black hole due to a scalar field is investigated by using the DLM scheme.The entropy is renormalized to the standard Bekenstein-Hawking formula with a one-loop correction arising from the higher curvature terms of the gravitational action. For the scalar field,the renormalized Newton constant and two renormalized coupling constants in the toroidal black hole are the same as those in the Reissner-Nordstrom black hole except for other one.
Quantum entropies of electromagnetic and gravitational fields on Taub-NUT black hole background
Institute of Scientific and Technical Information of China (English)
LIU Xiao-ying; XIAO Shi-fa; LI Fang-yu
2005-01-01
The main characteristics and Petrov type of Taub-NUT spacetime are studied, and the quantum entropy of Taub-NUT black hole due to electromagnetic and gravitational fields is calculated via brick-wall model. It is shown that the quantum entropy has both the linearly and the logarithmically divergent terms. For electromagnetic field, these terms depend on the characteristic of the black hole; while for gravitational field, they depend not only on the characteristic of the black hole but also on the spin of the fields.
Entropy increase law for black holes in Lanczos-Lovelock gravity
Kolekar, Sanved; Sarkar, Sudipta
2012-01-01
We study the physical process version of first law of black hole thermodynamics within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of the stationary black holes in Lanczos-Lovelock gravity can never decrease for quasi-stationary processes in which the horizon is perturbed by the accretion of positive energy matter. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelock models and takes a step towards proving the analogue of the black hole area increase-theorem in a wider class of gravitational theories.
Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes
Energy Technology Data Exchange (ETDEWEB)
Sfetsos, K. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Skenderis, K. [Instituut voor Theoretische Fysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium)
1998-04-27
We derive the Bekenstein-Hawking entropy formula for four- and five-dimensional non-supersymmetric black holes (which include the Schwarzchild ones) by counting microscopic states. This is achieved by first showing that these black holes are U-dual to the three-dimensional black hole of Banados-Teitelboim-Zanelli and then counting microscopic states of the latter following Carlip`s approach. Black holes higher than five dimensional are also considered. We discuss the connection of our approach to the D-brane picture. (orig.) 56 refs.
Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes
Sfetsos, K
1998-01-01
We derive the Bekenstein--Hawking entropy formula for four and five dimensional non-supersymmetric black holes (which include the Schwarzchild ones) by counting microscopic states. This is achieved by first showing that these black holes are U-dual to the three-dimensional black hole of Banados--Teitelboim--Zanelli and then counting microscopic states of the latter following Carlip's approach. Higher than five dimensional black holes are also considered. We discuss the connection of our approach to the D-brane picture.
Entropy bound of horizons for accelerating, rotating and charged Plebanski-Demianski black hole
Debnath, Ujjal
2016-09-01
We first review the accelerating, rotating and charged Plebanski-Demianski (PD) black hole, which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou-Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole.
Membrane paradigm and entropy of black holes in the Euclidean action approach
Lemos, José P S
2011-01-01
The membrane paradigm approach to black holes fixes in the vicinity of the event horizon a fictitious surface, the stretched horizon, so that the spacetime outside remains unchanged and the spacetime inside is vacuum. Using this powerful method, several black hole properties have been found and settled, such as the horizon's viscosity, electrical conductivity, resistivity, as well as other properties. On the other hand the Euclidean action approach to black hole spacetimes has been very fruitful in understanding black hole entropy. Combining both the Euclidean action and membrane paradigm approaches a direct derivation of the black hole entropy is given. In the derivation it is considered that the only fields present are the gravitational and matter fields, with no electric field.
Empty Black Holes, Firewalls, and the Origin of Bekenstein-Hawking Entropy
Saravani, Mehdi; Mann, Robert B
2012-01-01
We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semi-classical solution to the cosmological constant problem(s), and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. We then demonstrate that positing a surface fluid with vanishing energy density (but non-vanishing pressure) at the new boundary of spacetime, which is required by Israel junction conditions, yields a thermodynamic entropy that is identical to the Bekenstein-Hawking area law for charged rotating black holes. To our knowledge, this is the first derivation of black hole entropy which only employs local thermodynamics. Fina...
Bosonic and fermionic entropy of black holes with different temperatures on horizon surface
Institute of Scientific and Technical Information of China (English)
Ding Tian-Ran; Wu Yue-Qin; Zhang Li-Chun
2004-01-01
By using the method of quantum statistics, we derive directly the partition functions of bosonic and fermionic field in the black hole space-time with different temperatures on horizon surface. The statistical entropy of the black hole is obtained by an improved brick-wall method. When we choose a proper parameter in our results, we can obtain that the entropy of the black hole is proportional to the area of horizon. In our result, there do not exist any neglected term or divergent logarithmic term as given in the original brick-wall method. We have avoided the difficulty in solving the wave equation of the scalar and Dirac field. A simple and direct way of studying entropy of the black hole is given.
An exploration of the black hole entropy via the Weyl tensor
Energy Technology Data Exchange (ETDEWEB)
Li, Nan [Northeastern University, Department of Physics, College of Sciences, Shenyang (China); Li, Xiao-Long [Beijing Normal University, Department of Astronomy, Beijing (China); Song, Shu-Peng [Beijing Normal University, Department of Physics, Beijing (China)
2016-03-15
The role of the Weyl tensor C{sub μνλρ} in black hole thermodynamics is explored by looking at the relation between the scalar invariant C{sub μνλρ}C{sup μνλρ} and the entropy of n-dimensional static black holes. It is found that this invariant can be identified as the entropy density of the gravitational fields for classical 5-dimensional black holes. We calculate the proper volume integrals of C{sub μνλρ}C{sup μνλρ} for the Schwarzschild and Schwarzschild-anti-de Sitter black holes and show that these integrals correctly lead to the Bekenstein-Hawking entropy formulas, only up to some coefficients. (orig.)
An exploration of the black hole entropy via the Weyl tensor
International Nuclear Information System (INIS)
The role of the Weyl tensor Cμνλρ in black hole thermodynamics is explored by looking at the relation between the scalar invariant CμνλρCμνλρ and the entropy of n-dimensional static black holes. It is found that this invariant can be identified as the entropy density of the gravitational fields for classical 5-dimensional black holes. We calculate the proper volume integrals of CμνλρCμνλρ for the Schwarzschild and Schwarzschild-anti-de Sitter black holes and show that these integrals correctly lead to the Bekenstein-Hawking entropy formulas, only up to some coefficients. (orig.)
Black Hole Entropy with and without Log Correction in Loop Quantum Gravity
International Nuclear Information System (INIS)
Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the calculations yield an entropy proportional to the area eigenvalue with no such correction when the area eigenvalue is large compared to the classical area
Black Hole Entropy with and without Log Correction in Loop Quantum Gravity
Mitra, P.
2014-06-01
Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the calculations yield an entropy proportional to the area eigenvalue with no such correction when the area eigenvalue is large compared to the classical area.
Black Hole Entropy with and without Log Correction in Loop Quantum Gravity
Energy Technology Data Exchange (ETDEWEB)
Mitra, P.
2014-06-15
Earlier calculations of black hole entropy in loop quantum gravity have given a term proportional to the area with a correction involving the logarithm of the area when the area eigenvalue is close to the classical area. However the calculations yield an entropy proportional to the area eigenvalue with no such correction when the area eigenvalue is large compared to the classical area.
Liu, Hang
2016-01-01
In this paper, we investigate the angular momentum independence of the entropy sum and product for AdS rotating black holes based on the first law of thermodynamics and a mathematical lemma related to Vandermonde determinant. The advantage of this method is that the explicit forms of the spacetime metric, black hole mass and charge are not needed but the Hawking temperature and entropy formula on the horizons are necessary for static black holes, while our calculations require the expressions of metric and angular velocity formula. We find that the entropy sum is always independent of angular momentum for all dimensions and the angular momentum-independence of entropy product only holds for the dimensions $d>4$ with at least one rotation parameter $a_i=0$, while the mass-free of entropy sum and entropy product for rotating black holes only stand for higher dimensions ($d>4$) and for all dimensions, respectively. On the other hand, we find that the introduction of a negative cosmological constant does not affe...
Entropy Spectrum of Black Holes of Heterotic String Theory via Adiabatic Invariance
Institute of Scientific and Technical Information of China (English)
Alexis Larra？ aga; Luis Cabarique; Manuel Londo？ o
2012-01-01
Using adiabatic invariance and the Bohr-Sommerfeld quantization rule we investigate the entropy spectroscopy of two black holes of heterotic string theory,the charged GMGHS and the rotating Sen solutions.It is shown that the entropy spectrum is equally spaced in both cases,identically to the spectrum obtained before for Schwarzschild,Reissner-Nordstr?m and Kerr black holes.Since the adiabatic invariance method does not use quasinormal mode analysis,there is no need to impose the small charge or small angular momentum limits and there is no confusion on whether the real part or the imaginary part of the modes is responsible for the entropy spectrum.
Entropy of Reissner–Nordström–de Sitter black hole
Directory of Open Access Journals (Sweden)
Li-Chun Zhang
2016-10-01
Full Text Available Based on the consideration that the black hole horizon and the cosmological horizon of Reissner–Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tend to coincide.
Entropy of Reissner-Nordström-de Sitter black hole
Zhang, Li-Chun; Zhao, Ren; Ma, Meng-Sen
2016-10-01
Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordström black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tend to coincide.
Near horizon symmetry and entropy of black holes in the presence of a conformally coupled scalar
Meng, Kun; Zhao, Liu
2014-01-01
We analyze the near horizon conformal symmetry for black hole solutions in gravity with a conformally coupled scalar field using the method proposed by Majhi and Padmanabhan recently. It is shown that the entropy of the black holes of the form $\\mathrm{d}s^2 = - f(r)\\mathrm{d}t^2 + \\mathrm{d}r^2/f(r)+...$ agrees with Wald entropy. This result is different from previous result obtained by M. Natsuume, T. Okamura and M. Sato using the canonical Hamiltonian formalism, which claims a discrepancy from Wald entropy.
Using clocks to determine the entropy of black holes and other space-time singularities
Ojo, A
2005-01-01
Space-time singularities, viz. Big bang, Big crunch and black holes have been shown to follow from the singularity theorems of General relativity. Whether the entropy at such infinite proper-time objects can be other than zero has also been a longstanding subject of research. Currently the property most commonly chosen to calculate their entropy is a multiple of the surface area of the event horizon and usually gives non-zero entropy values. Though popular, this choice still leaves some substantial questions unanswered hence the motivation for alternative methods for entropy derivation. Here, we use a different property, the proper-time at singularities based on the General relativity predicted behavior of clocks, to derive their entropy. We find, firstly within statistical and thermodynamic principles, secondly when this property is taken into account in the Bekenstein-Hawking formula and thirdly illustrating with a natural analogue, that the entropy of black holes and all other gravitational singularities c...
Yan, Hao-Peng; Liu, Wen-Biao
2016-08-01
Using Parikh-Wilczek tunneling framework, we calculate the tunneling rate from a Schwarzschild black hole under the third order WKB approximation, and then obtain the expressions for emission spectrum and black hole entropy to the third order correction. The entropy contains four terms including the Bekenstein-Hawking entropy, the logarithmic term, the inverse area term, and the square of inverse area term. In addition, we analyse the correlation between sequential emissions under this approximation. It is shown that the entropy is conserved during the process of black hole evaporation, which consists with the request of quantum mechanics and implies the information is conserved during this process. We also compare the above result with that of pure thermal spectrum case, and find that the non-thermal correction played an important role.
Entanglement entropy of black holes and anti-de Sitter space/conformal-field-theory correspondence.
Solodukhin, Sergey N
2006-11-17
A recent proposal by Ryu and Takayanagi for a holographic interpretation of entanglement entropy in conformal field theories dual to supergravity on anti-de Sitter space is generalized to include entanglement entropy of black holes living on the boundary of anti-de Sitter space. The generalized proposal is verified in boundary dimensions d=2 and d=4 for both the uv-divergent and uv-finite terms. In dimension d=4 an expansion of entanglement entropy in terms of size L of the subsystem outside the black hole is considered. A new term in the entropy of dual strongly coupled conformal-field theory, which universally grows as L(2)lnL and is proportional to the value of the obstruction tensor at the black hole horizon, is predicted. PMID:17155672
Entropy Bound of Horizons for Accelerating, Rotating and Charged Plebanski-Demianski Black Hole
Debnath, Ujjal
2015-01-01
We first review the accelerating, rotating and charged Plebanski-Demianski (PD) black hole, which includes the Kerr-Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product are found for event horizon and Cauchy horizon. Also their sums are also found for both horizons. All these relations are found to be depend on mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons are investigated. Also we found the Christodoulou-Ruffini mass for extremal PD black hole. Finally, using first law of thermodynami...
Empty black holes, firewalls, and the origin of Bekenstein-Hawking entropy
Saravani, Mehdi; Afshordi, Niayesh; Mann, Robert B.
2014-01-01
We propose a novel solution for the endpoint of gravitational collapse, in which spacetime ends (and is orbifolded) at a microscopic distance from black hole event horizons. This model is motivated by the emergence of singular event horizons in the gravitational aether theory, a semiclassical solution to the cosmological constant problem(s) and thus suggests a catastrophic breakdown of general relativity close to black hole event horizons. A similar picture emerges in fuzzball models of black holes in string theory, as well as the recent firewall proposal to resolve the information paradox. We then demonstrate that positing a surface fluid in thermal equilibrium with Hawking radiation, with vanishing energy density (but nonvanishing pressure) at the new boundary of spacetime, which is required by Israel junction conditions, yields a thermodynamic entropy that is identical to the Bekenstein-Hawking area law, SBH, for charged rotating black holes. To our knowledge, this is the first derivation of black hole entropy that only employs local thermodynamics. Furthermore, a model for the microscopic degrees of freedom of the surface fluid (which constitute the microstates of the black hole) is suggested, which has a finite, but Lorentz-violating, quantum field theory. Finally, we comment on the effects of physical boundary on Hawking radiation and show that relaxing the assumption of equilibrium with Hawking radiation sets SBH as an upper limit for Black Hole entropy.
Intrinsic Topological Structure of Entropy of Kerr Black Holes%Kerr黑洞熵的内禀拓扑结构
Institute of Scientific and Technical Information of China (English)
颜继江; 杨国宏; 田立君
2005-01-01
In the light of φ-mapping method and the relationship between entropy and the Euler characteristic, the intrinsic topological structure of entropy of Kerr black holes is studied. From the Gauss-Bonnet-Chern theorem, it is shown that the entropy of Kerr black hole is determined by singularities of the Killing vector field of spacetime. These singularities naturally carry topological numbers, Hopf indices and Brouwer degrees, which can also be viewed as topological quantization of entropy of Kerr black holes. Specific results S =A/4 for non-extreme Kerr black holes and S = 0 for extreme ones are calculated independently by using the above-mentioned methods.
Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
Gupta, Kumar S; Jurić, Tajron; Meljanac, Stjepan; Samsarov, Anđelo
2015-01-01
We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that noncommutativity introduces a non-equispaced in the (discrete) area and entropy spectra.
Area(or Entropy) Product Formula for a Regular Black Hole
Pradhan, Parthapratim
2015-01-01
We compute the area(or entropy) product formula for a regular black hole derived by Ay\\'on-Beato and Garc\\'ia in 1998\\cite{abg}. By explicit and exact calculation, it is shown that the entropy product formula of two physical horizons strictly \\emph{depends} upon the ADM mass parameter that means it is \\emph{not} an universal(mass-independent) quantity. But a slightly more complicated function of event horizon area and Cauchy horizon area is indeed a \\emph{mass-independent} quantity. We also compute other thermodynamic properties of the said black hole. We further study the stability of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses second order phase transition. The pictorial diagram of the phase transition is given.
Black hole entropy in loop quantum gravity: The role of internal symmetries
Energy Technology Data Exchange (ETDEWEB)
Barbero G, J Fernando, E-mail: fbarbero@iem.cfmac.csic.e [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain)
2009-06-01
I will discuss here the role of the internal symmetry group in the computations of black hole entropy in loop quantum gravity according to the standard prescription given by Domagala and Lewandowski. In particular I will show how it is possible to take into account the possible choice of either SO(3) or SU(2) as the internal symmetry groups of general relativity in Loop Quantum Gravity and how this choice changes the combinatorial problem of counting the black hole degrees of freedom.
An Exploration of the Black Hole Entropy via the Weyl Tensor
Li, Nan; Song, Shu-Peng
2015-01-01
The Weyl tensor is the trace-free part of the Riemann tensor. Therefore, it is independent of the energy-momentum tensor and is thus not linked to the dynamics of gravitational fields. In this paper, we explore its possible thermodynamical property (i.e. its relationship with the black hole entropy). For a Schwarzschild black hole, the Weyl scalar invariant, $C_{\\mu\
Semiclassical corrections to black hole entropy and the generalized uncertainty principle
Directory of Open Access Journals (Sweden)
Pedro Bargueño
2015-03-01
Full Text Available In this paper, employing the path integral method in the framework of a canonical description of a Schwarzschild black hole, we obtain the corrected inverse temperature and entropy of the black hole. The corrections are those coming from the quantum effects as well as from the Generalized Uncertainty Principle effects. Furthermore, an equivalence between the polymer quantization and the Generalized Uncertainty Principle description is shown provided the parameters characterizing these two descriptions are proportional.
Entropy emission properties of near-extremal Reissner-Nordström black holes
Hod, Shahar
2016-05-01
Bekenstein and Mayo have revealed an interesting property of evaporating (3 +1 )-dimensional Schwarzschild black holes: their entropy emission rates S˙Sch are related to their energy emission rates P by the simple relation S˙Sch=CSch×(P /ℏ)1/2, where CSch is a numerically computed dimensionless coefficient. Remembering that (1 +1 )-dimensional perfect black-body emitters are characterized by the same functional relation, S˙1 +1=C1 +1×(P /ℏ)1/2 [with C1 +1=(π /3 )1/2], Bekenstein and Mayo have concluded that, in their entropy emission properties, (3 +1 )-dimensional Schwarzschild black holes behave effectively as (1 +1 )-dimensional entropy emitters. Later studies have shown that this intriguing property is actually a generic feature of all radiating (D +1 )-dimensional Schwarzschild black holes. One naturally wonders whether all black holes behave as simple (1 +1 )-dimensional entropy emitters? In order to address this interesting question, we shall study in this paper the entropy emission properties of Reissner-Nordström black holes. We shall show, in particular, that the physical properties which characterize the neutral sector of the Hawking emission spectra of these black holes can be studied analytically in the near-extremal TBH→0 regime (here TBH is the Bekenstein-Hawking temperature of the black hole). We find that the Hawking radiation spectra of massless neutral scalar fields and coupled electromagnetic-gravitational fields are characterized by the nontrivial entropy-energy relations S˙RNScalar=-CRNScalar×(A P3/ℏ3)1/4ln (A P /ℏ) and S˙RN Elec -Grav=-CRNElec -Grav×(A4P9/ℏ9)1 /10ln (A P /ℏ) in the near-extremal TBH→0 limit (here {CRNScalar,CRNElec -Grav} are analytically calculated dimensionless coefficients and A is the surface area of the Reissner-Nordström black hole). Our analytical results therefore indicate that not all black holes behave as simple (1 +1 )-dimensional entropy emitters.
On the computation of black hole entropy in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Fernando Barbero G, J [Instituto de Estructura de la Materia, CSIC, Serrano 123, 28006 Madrid (Spain); Villasenor, Eduardo J S, E-mail: fbarbero@iem.cfmac.csic.e, E-mail: ejsanche@math.uc3m.e [Instituto Gregorio Millan, Grupo de Modelizacion y Simulacion Numerica, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganes (Spain)
2009-02-07
We discuss some issues related to the computation of black hole entropy in loop quantum gravity from the novel point of view provided by the recent number-theoretical methods introduced by the authors and their collaborators. In particular we give exact expressions, in the form of integral transforms, for the black hole entropy in terms of the area. We do this by following several approaches based both on our combinatorial techniques and on functional equations similar to those employed by Meissner in his pioneering work on this subject. To put our results in perspective, we compare them with those of Meissner. We will show how our methods confirm some of his findings, extend the validity of others and correct some mistakes. At the end of the paper, we will discuss the delicate issue of the asymptotics of black hole entropy.
The entropy emission properties of near-extremal Reissner-Nordstr\\"om black holes
Hod, Shahar
2016-01-01
Bekenstein and Mayo have revealed an interesting property of evaporating $(3+1)$-dimensional Schwarzschild black holes: their entropy emission rates $\\dot S_{\\text{Sch}}$ are related to their energy emission rates $P$ by the simple relation $\\dot S_{\\text{Sch}}=C_{\\text{Sch}}\\times (P/\\hbar)^{1/2}$. Remembering that $(1+1)$-dimensional perfect black-body emitters are characterized by the same functional relation, $\\dot S^{1+1}=C^{1+1}\\times(P/\\hbar)^{1/2}$, Bekenstein and Mayo have concluded that, in their entropy emission properties, $(3+1)$-dimensional Schwarzschild black holes behave effectively as $(1+1)$-dimensional entropy emitters. One naturally wonders whether all black holes behave as simple $(1+1)$-dimensional entropy emitters? In order to address this interesting question, we shall study in this paper the entropy emission properties of Reissner-Nordstr\\"om black holes. We shall show, in particular, that the physical properties which characterize the neutral sector of the Hawking emission spectra of...
The universal property of the entropy sum of black holes in all dimensions
Directory of Open Access Journals (Sweden)
Yi-Qiang Du
2014-12-01
Full Text Available It is proposed by Cvetic et al. [1] that the product of all horizon areas for general rotating multi-change black holes has universal expressions independent of the mass. When we consider the product of all horizon entropies, however, the mass will be present in some cases, while another new universal property [2] is preserved, which is more general and says that the sum of all horizon entropies depends only on the coupling constants of the theory and the topology of the black hole. The property has been studied in limited dimensions and the generalization in arbitrary dimensions is not straight-forward. In this Letter, we prove a useful formula, which makes it possible to investigate this conjectured universality in arbitrary dimensions for the maximally symmetric black holes in general Lovelock gravity and f(R gravity. We also propose an approach to compute the entropy sum of general Kerr–(anti-de-Sitter black holes in arbitrary dimensions. In all these cases, we prove that the entropy sum depends only on the coupling constants and the topology of the black hole.
The universal property of the entropy sum of black holes in all dimensions
International Nuclear Information System (INIS)
It is proposed by Cvetic et al. [1] that the product of all horizon areas for general rotating multi-change black holes has universal expressions independent of the mass. When we consider the product of all horizon entropies, however, the mass will be present in some cases, while another new universal property [2] is preserved, which is more general and says that the sum of all horizon entropies depends only on the coupling constants of the theory and the topology of the black hole. The property has been studied in limited dimensions and the generalization in arbitrary dimensions is not straight-forward. In this Letter, we prove a useful formula, which makes it possible to investigate this conjectured universality in arbitrary dimensions for the maximally symmetric black holes in general Lovelock gravity and f(R) gravity. We also propose an approach to compute the entropy sum of general Kerr–(anti-)de-Sitter black holes in arbitrary dimensions. In all these cases, we prove that the entropy sum depends only on the coupling constants and the topology of the black hole
Thermodynamic Products for Einstein-Gauss-Bonnet Black Hole with {\\alpha}-Corrected Entropy Term
Mandal, Abhijit; Biswas, Ritabrata(Indian Institute of Engineering Sceince and Technology Shibpur (Formerly, Bengal Engineering and Science University Shibpur), 711 013, Howrah, West Bengal, India)
2015-01-01
In the present work, we consider a charged black hole in five dimensional Einstein-Gauss-Bonnet gravity where the {\\alpha} corrected entropy term is considered. We examine the horizon radii product, entropy product, Hawking temperature product and free energy product for both event horizon and Cauchy horizon. Our motive is to check whether the same quantity for event horizon and Cauchy horizon is free of mass, i.e., global or not. We further study the stability of such black hole by computing...
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
Energy Technology Data Exchange (ETDEWEB)
Anacleto, M.A., E-mail: anacleto@df.ufcg.edu.br; Brito, F.A., E-mail: fabrito@df.ufcg.edu.br; Passos, E., E-mail: passos@df.ufcg.edu.br; Santos, W.P.
2014-10-07
In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when λ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
International Nuclear Information System (INIS)
In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when λ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
Directory of Open Access Journals (Sweden)
M.A. Anacleto
2014-10-01
Full Text Available In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when λ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
Anacleto, M. A.; Brito, F. A.; Passos, E.; Santos, W. P.
2014-10-01
In this paper we investigate statistical entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when λ introduced in the generalized uncertainty principle takes a specific value. However, in this method, it is not needed to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.
The entropy of the noncommutative acoustic black hole based on generalized uncertainty principle
Anacleto, M A; Passos, E; Santos, W P
2014-01-01
In this paper we investigate statistics entropy of a 3-dimensional rotating acoustic black hole based on generalized uncertainty principle. In our results we obtain an area entropy and a correction term associated with the noncommutative acoustic black hole when $ \\lambda $ introduced in the generalized uncertainty principle takes a specific value. However, in this method, is not need to introduce the ultraviolet cut-off and divergences are eliminated. Moreover, the small mass approximation is not necessary in the original brick-wall model.
A note on renormalization and black hole entropy in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Jacobson, Ted [Department of Physics, University of Maryland, College Park, MD 20742-4111 (United States)
2007-09-21
Microscopic state counting for a black hole in loop quantum gravity yields a result proportional to the horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein-Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds. (comments, replies and notes)
Fate of Three-Dimensional Black Holes Coupled to a Scalar Field and the Bekenstein-Hawking Entropy
Park, M I
2004-01-01
Three-dimensional black holes coupled to a self-interacting scalar field is considered. It is known that its statistical entropy $a' la$ Strominger does $not$ agree with the Bekenstein-Hawking (BH) entropy. However I show that, by a careful treatment of the vacuum state in the {\\it canonical} ensemble with a fixed temperature, which is the same as that of the BTZ black hole without the scalar field, the BH entropy is exactly produced by the Cardy's formula. I discuss its several implications, including the fate of black holes, no-scalar-hair theorems, stability, mirror black holes, and one-loop corrections.
Two aspects of black hole entropy in Lanczos-Lovelock models of gravity
Kolekar, Sanved; Kothawala, Dawood; Padmanabhan, T.
2012-03-01
We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein’s theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic), we use a procedure motivated by earlier work by Pretorius, Vollick, and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific mth-order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic), we generalize a procedure, previously introduced by Padmanabhan in the context of general relativity, to study off-shell entropy of a class of metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.
Black hole entropy and SU(2) Chern-Simons theory
Engle, Jonathan; Noui, Karim; Perez, Alejandro
2009-01-01
Black holes in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points. Moreover, the counting can be mapped to counting the number of SU(2) intertwiners compatible with the...
Logarithmic Corrections to the Black Hole Entropy Product of ${\\cal H}^{\\pm}$ via Cardy Formula
Pradhan, Parthapratim
2016-01-01
We compute the logarithmic corrections to the black hole (BH) entropy product of ${\\cal H}^{\\pm}$ \\footnote{ ${\\cal H}^{+}$ and ${\\cal H}^{-}$ denote outer (event) horizon and inner (Cauchy) horizons} by using \\emph{Cardy prescription}. We particularly apply this formula for BTZ BH. We show that logarithmic corrections to the entropy product of ${\\cal H}^{\\pm}$ when computed \\emph{via Cardy formula} it does not mass-independent (universal) nor does it quantized.
The combinatorics of the SU(2) black hole entropy in loop quantum gravity
Agullo, Ivan; Borja, Enrique F; Diaz-Polo, Jacobo; Villaseñor, Eduardo J S
2009-01-01
We use the combinatorial and number-theoretical methods developed in previous work by the authors to study black hole entropy in the new proposal put forward by Engle, Noui and Perez. Specifically we give the generating functions relevant for the computation of the entropy and use them to derive its asymptotic behavior including the value of the Immirzi parameter and the coefficient of the logarithmic correction.
Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity
Kolekar, Sanved; Padmanabhan, T
2011-01-01
We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein's theory and generalize them to Lanczos-Lovelock models. In the first approach (which could be called extrinsic) we use a procedure motivated by earlier work by Pretorius, Vollick and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific m-th order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down ...
Quantum-Corrected Two-Dimensional Horava-Lifshitz Black Hole Entropy
Directory of Open Access Journals (Sweden)
M. A. Anacleto
2016-01-01
Full Text Available We focus on the Hamilton-Jacobi method to determine several thermodynamic quantities such as temperature, entropy, and specific heat of two-dimensional Horava-Lifshitz black holes by using the generalized uncertainty principles (GUP. We also address the product of horizons, mainly concerning the event, Cauchy, and cosmological and virtual horizons.
Entropy of near-extremal black holes in AdS_5
V. Balasubramanian; J. de Boer; V. Jejjala; J. Simón
2008-01-01
We construct the microstates of near-extremal black holes in AdS_5 x S^5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S^5, and we show that they dominate the entropy by directly enumerati
Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: Scalar Field Case
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2001-01-01
The total quantum statistical entropy of Reissner-Nordstrom (RN) black holes is evaluated. The spacetime of the black holes is divided into three regions-region 1, (r ＞ ro); region 2, (ro ＞ r ＞ ri);andregion 3, (ri ＞ r ＞ 0)-where ro is the radius of the outer event horizon, and ri is the radius of the inner event horizon. The total quantum statistical entropy of RN black holes is S = S1 + S2 + Ss, where Si (i = 1, 2, 3) is the entropy, contributed by region Si (i = 1, 2, 3). The detailed calculation shows that S2 ≈ 0. S1 = (π2/45)[kbAo/∈2β3], S3 = -(r2/45)[kbAi/∈2βs], where Ao and Ai are, respectively, the area of the outer and inner event horizons. Thus, as ri approaches ro, in the extreme case the total quantum statistical entropy of RN black holes approaches zero.
Entropy Correction for Cosmological Horizon of Schwarzschild-de Sitter Black Holes
Institute of Scientific and Technical Information of China (English)
LIU Bai-Sheng; ZHANG Jing-Yi
2011-01-01
In this paper, we first calculate the emission rate of the massive particles' de Sitter tunneling across the cosmological horizon of Schwarzschild-de Sitter black holes to the second order accuracy. Then, by assuming the emission process satisfies an underlying unitary theory, we have obtained the corrected entropy for cosmological horizon. Finally,a discussion about the de Sitter tunneling is presented.
Total Quantum Statistical Entropy of Reissner-Nordstrom Black Holes: in Dirac Field Case
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2005-01-01
The total quantum statistical entropy of Reissner-Nordstrom black holes in Dirac field case is evaluated in this article. The space-time of the black holes is divided into three regions: region 1 (r ＞ ro), region 2 (ro ＞ r ＞ ri),and region 3 (ri ＞ r ＞ 0), where ro is the radius of the outer event horizon, and ri is the radius of the inner event horizon. The total quantum statistical entropy of Reissner-Nordstrom black holes is S = S1 + S2 + S3, where Si(i ＝ 1, 2, 3) is the entropy, contributed by regions 1, 2, 3. The detailed calculation shows that S2 is neglectfully sma//.S1 = wt(π2/45)kb(Ao/ε2β3), S3 = -wt(π2/45)kb(Ai/ε2β3), where Ao and Ai are, respectively, the areas of the outer and inner event horizons, wt ＝ 2s[1 - 2-(s+1)], s ＝ d/2, d is the space-time dimension, here d ＝ 4, s ＝ 2. As ri approaches ro in the extreme case the total quantum statistical entropy of Reissner-Nordstrom black holes approaches zero.
Phase transition and entropy inequality of noncommutative black holes in a new extended phase space
Miao, Yan-Gang
2016-01-01
We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as {\\em the noncommutative pressure}. In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former takes a UV effect while the latter does an IR effect, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.
R\\'enyi entropy and the thermodynamic stability of black holes
Czinner, Viktor G
2016-01-01
Thermodynamic stability of black holes, described by the R\\'enyi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking-Page-like black hole phase transition occurs at a critical temperature which depends on the $q$-parameter of the R\\'enyi formula.
Quantum correction of the Dirac field to the entropy of a static black hole
Xiang, Li
2001-12-01
The one-loop effective action for the quantum Dirac field is regulated by Pauli-Villars scheme, and the renormalized action for the coupled gravitational-quantum Dirac field is obtained. The quantum entropy of the massive Dirac field outside a static black hole is calculated by Rindler approximation. The divergencies of the free energy and entropy are regulated by the large mass of some fictitious regulators. The divergent entropy is renormalizable and yields the standard Bekenstein-Hawking formula, in terms of the Newton's constant.
Extremal Black Holes in Supergravity and the Bekenstein-Hawking Entropy
Directory of Open Access Journals (Sweden)
R. D'Auria
2002-03-01
Full Text Available Abstract: We review some results on the connection among supergravity central charges, BPS states and Bekenstein-Hawking entropy. In particular, N = 2 super-gravity in four dimensions is studied in detail. For higher N supergravities we just give an account of the general theory specializing the discussion to the N = 8 case when one half of supersymmetry is preserved. We stress the fact that for extremal supergravity black holes the entropy formula is topological, that is the entropy turns out to be a moduli independent quantity and can be written in terms of invariants of the duality group of the supergravity theory.
Sun, Yuan; Zhao, Liu
2016-01-01
The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane. On the boundary, we calculated the regularized HEE of a disk region of different sizes. We find strong numerical evidence for the failure of equal area law for isobaric curves on the temperature-HEE plane and for the correctness of first law of entanglement entropy, and briefly give an explanation for why the latter may serve as a reason for the former, i.e. the failure of equal area law on the temperature-HEE plane.
International Nuclear Information System (INIS)
We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole
Entropy Spectrum of a KS Black Hole in IR Modified Hořava-Lifshitz Gravity
International Nuclear Information System (INIS)
As a renormalizable theory of gravity, Hořava-Lifshitz gravity, might be an ultraviolet completion of general relativity and reduces to Einstein gravity with a nonvanishing cosmological constant in infrared. Kehagias and Sfetsos obtained a static spherically symmetric black hole solution called KS black hole in the IR modified Hořava-Lifshitz theory. In this paper, the entropy spectrum and area spectrum of a KS black hole are investigated based on the proposal of adiabatic invariant quantity. By calculating the action of producing a pair of particles near the horizon, it is obtained that the action of the system is exactly equivalent to the change of black hole entropy, which is an adiabatic invariant quantity. With the help of Bohr-Sommerfeld quantization rule, it is concluded that the entropy spectrum is discrete and equidistant spaced and the area spectrum is not equidistant spaced, which depends on the parameter of gravity theory. Some summary and discussion will be given in the last
Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity
Kloster, S.; Brannlund, J.; DeBenedictis, A.
2007-01-01
In the context of loop quantum gravity, we construct the phase-space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase-space is calculated including the genus cycles as degrees of freedom. From this, the black hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading ter...
Phase space and black-hole entropy of higher genus horizons in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Kloster, S [Centre for Experimental and Constructive Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Brannlund, J [Department of Mathematics and Statistics, Dalhousie University, Halifax, NS B3H 3J5 (Canada); DeBenedictis, A [Pacific Institute for the Mathematical Sciences, Simon Fraser University Site, Burnaby, BC V5A 1S6 (Canada)], E-mail: stevek@sfu.ca, E-mail: johanb@mathstat.dal.ca, E-mail: adebened@sfu.ca
2008-03-21
In the context of loop quantum gravity, we construct the phase space of isolated horizons with genus greater than 0. Within the loop quantum gravity framework, these horizons are described by genus g surfaces with N punctures and the dimension of the corresponding phase space is calculated including the genus cycles as degrees of freedom. From this, the black-hole entropy can be calculated by counting the microstates which correspond to a black hole of fixed area. We find that the leading term agrees with the A/4 law and that the sub-leading contribution is modified by the genus cycles.
Conserved charges, surface degrees of freedom, and black hole entropy
Seraj, Ali
2016-01-01
In this thesis, we study the Hamiltonian and covariant phase space description of gravitational theories. The phase space represents the allowed field configurations and is accompanied by a closed nondegenerate 2 form- the symplectic form. We will show that local/gauge symmetries of the action fall into two different categories in the phase space formulation. Those corresponding to constraints in the phase space, and those associated with nontrivial conserved charges. We argue that while the former is related to redundant gauge degrees of freedom, the latter leads to physically distinct states of the system, known as surface degrees of freedom and can induce a lower dimensional dynamics on the system. These ideas are then implemented to build the phase space of specific gravitational systems: 1) asymptotically AdS3 spacetimes, and 2) near horizon geometries of extremal black holes (NHEG) in arbitrary dimension. In the AdS3 phase space, we show that Brown-Henneaux asymptotic symmetries can be extended inside t...
Refined holographic entanglement entropy for the AdS solitons and AdS black holes
International Nuclear Information System (INIS)
We consider the refinement of the holographic entanglement entropy for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss–Bonnet term. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy, the so-called renormalized entanglement entropy which is independent of the choices of UV cutoff. Our main results are: (i) the renormalized entanglement entropies of the AdSd+1 soliton for d=4,5 are neither monotonically decreasing along the RG flow nor positive-definite, especially around the deconfinement/confinement phase transition; (ii) there is no topological entanglement entropy for AdS5 soliton even with Gauss–Bonnet correction; (iii) for the AdS black holes, the renormalized entanglement entropy obeys an expected volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover even with Gauss–Bonnet correction; (iv) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state
Reissner-Nordstrom Black Hole Entropy Inside and Outside the Brick Wall
Institute of Scientific and Technical Information of China (English)
刘文彪
2003-01-01
Applying the generalized uncertainty relation to the calculation of the free energy and entropy of a Reissner Nordstrom black hole inside the brick wall, the entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon. This is compared with the entropy calculated via the original brick wall model. The entropy given by the original brick wall model comes from the outside of the brick wall seemingly.The inside result using generalized uncertainty relation is similar to the outside result using original uncertainty relation, and the divergence inside the brick wall disappears. It is apparent that the cutoff is something related to the quantum theory of gravity.
The Generalized Uncertainty Principle and Black Hole Entropy in Tunneling formalism
Majumder, Barun
2013-01-01
In this Letter we study the effects of the Generalized Uncertainty Principle in the tunneling formalism for Hawking radiation to evaluate the quantum-corrected Hawking temperature and entropy for a Schwarzchild black hole. We compare our results with the existing results given by other candidate theories of quantum gravity. In the entropy-area relation we found some new corection terms and in the leading order we found a term which varies as the square-root of Area. We also get the well known logarithmic correction in the sub-leading order. We discuss the significance of this new quantum corrected leading order term.
Entropy of the Schwarzschild Black Hole in the Painlevé and the Lemaitre Coordinates
Institute of Scientific and Technical Information of China (English)
JING Ji-Liang; CHEN Song-Bai
2004-01-01
@@ In the Painlevé and the Lemaitre coordinates, the statistical-mechanical entropies of the Schwarzschild black hole arising from the quantum scalar field are investigated by using the 't Hooft's brick wall model At first sight,it seems that the results would be different from that in the standard Schwarzschild coordinate since both the Painlevé and the Lemaitre spacetimes do not possess the event horizon obviously. However, we prove that the entropies in these coordinates are exactly equivalent to that in the Schwarzschild coordinate.
Institute of Scientific and Technical Information of China (English)
DING Chi-Kun; JING Ji-Liang
2007-01-01
@@ The statistical-mechanical entropies of the Schwarzschild black hole arising from the scalar, Weyl neutrino, electromagnetic, Rarita-Schwinger and gravitational fields are investigated in the Painlevé and Lernaitre coordinates.Although the metrics in the Painlevé and the Lemaitre coordinates do not obviously possess the singularity as that in the Schwarzschild coordinate, we find that the entropies of the arbitrary spin fields in both the Painlevé and Lemaitre coordinates are exactly equivalent to that in the Schwarzschild coordinate.
Institute of Scientific and Technical Information of China (English)
HAN Yi-Wen; LIU Shou-Yu
2005-01-01
@@ The new equation of state density is obtained by the utilization of the generalized uncertainty relation. With the help of coordinates and the Wentzel-Kramers-Brillouin approximation, direct calculation of the scalar field entropy of the non-state black hole with an internal global monopole is performed. The entropy obtained from the calculation is proportional to the horizon area. The calculation can be free from convergence if without any cutoff, which is different from the brick-wall method. However, the pertinent result is limited.
Entropy of near-extremal black holes in AdS5
Energy Technology Data Exchange (ETDEWEB)
Simon, Joan; Balasubramanian, Vijay; de Boer, Jan; Jejjala, Vishnu; Simon, Joan
2007-07-24
We construct the microstates of near-extremal black holes in AdS_5 x S5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S5, and we show that they dominate the entropy by directly enumerating them and comparing the results with a partition sum calculation. We display new decoupling limits in which the field theory of the lightest open strings on the D-branes becomes dual to a near-horizon region of the black hole geometry. In the single-charge black hole we find evidence for an infrared duality between SU(N) Yang-Mills theories that exchanges the rank of the gauge group with an R-charge. In the two-charge case (where pairs of branes intersect on a line), the decoupled geometry includes an AdS_3 factor with a two-dimensional CFT dual. The degeneracy in this CFT accounts for the black hole entropy. In the three-charge case (where triples of branes intersect at a point), the decoupled geometry contains an AdS_2 factor. Below a certain critical mass, the two-charge system displays solutions with naked timelike singularities even though they do not violate a BPS bound. We suggest a string theoretic resolution of these singularities.
Entropy function from the gravitational surface action for an extremal near horizon black hole
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan [Indian Institute of Technology, Department of Physics, Guwahati, Assam (India)
2015-11-15
It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. the derivation of the Einstein's equations, the surface term calculated on the horizon leads to the entropy, etc. Here I investigate the role of it in the context of the entropy function and the entropy of extremal near horizon black holes. Considering only the Gibbons-Hawking-York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such a function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that the gravitational action is of a ''holographic'' nature - the surface term contains information of the bulk. (orig.)
Entropy function from the gravitational surface action for an extremal near horizon black hole
Energy Technology Data Exchange (ETDEWEB)
Majhi, Bibhas Ranjan, E-mail: bibhas.majhi@iitg.ernet.in [Department of Physics, Indian Institute of Technology, 781039, Guwahati, Assam (India)
2015-11-02
It is often argued that all the information of a gravitational theory is encoded in the surface term of the action; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action. This has been observed in various instances; e.g. the derivation of the Einstein’s equations, the surface term calculated on the horizon leads to the entropy, etc. Here I investigate the role of it in the context of the entropy function and the entropy of extremal near horizon black holes. Considering only the Gibbons–Hawking–York (GHY) surface term to define an entropy function for the extremal near horizon black hole solution, it is observed that the extremization of such a function leads to the exact value of the horizon entropy. This analysis again supports the previous claim that the gravitational action is of a “holographic” nature – the surface term contains information of the bulk.
Statistical analysis of entropy correction from topological defects in Loop Black Holes
Lochan, Kinjalk
2012-01-01
In this paper we discuss the entropy of quantum black holes in the LQG formalism when the number of punctures on the horizon is treated as a quantum hair, that is we compute the black hole entropy in the grand canonical (area) ensemble. The entropy is a function of both the average area and the average number of punctures and bears little resemblance to the Bekenstein-Hawking entropy. In the thermodynamic limit, both the "temperature" and the chemical potential can be shown to be functions only of the average area per puncture. At a fixed temperature, the average number of punctures becomes proportional to the average area and we recover the Bekenstein-Hawking area-entropy law to leading order provided that the Barbero-Immirzi parameter, $\\gamma$, is appropriately fixed. This also relates the chemical potential to $\\gamma$. We obtain a sub-leading correction, which differs in signature from that obtained in the microcanonical and canonical ensembles in its sign but agrees with earlier results in the grand can...
Considering boundary conditions for black hole entropy in loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Tamaki, Takashi [Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan)
2007-08-07
We argue for black hole entropy in loop quantum gravity (LQG) by taking into account the interpretation that there is no other side of the horizon. This gives new values for the Barbero-Immirzi parameter ({gamma} = 0.367 . .. or 0.323 . ..) which are larger than those considered before ({gamma} = 0.261 . .. or 0.237 . ..). We also discuss its consequences for future experiments.
Banerjee, S.; Gupta, R.K.; Mandal, I.; Sen, A.
2011-01-01
We compute logarithmic corrections to the entropy of supersymmetric extremal black holes in {N} = {4} and {N} = {8} supersymmetric string theories and find results in perfect agreement with the microscopic results. In particular these logarithmic corrections vanish for quarter BPS black holes in {N}
Note on Stability and Holographic Renyi Entropy in New Hyperbolic AdS Black Holes
Fang, Zhen; Li, Danning
2016-01-01
We construct a series of new hyperbolic black hole solutions in Einstein-Dilaton system and we apply holographic approach to investigate the spherical Renyi entropy in various deformations. Especially, we introduce various powers in the scalar potential for massive and massless scalar cases. These scalar potentials correspond to deformation of dual CFTs. We make use of a systematic way to generate numerical hyperbolic AdS black hole solutions. Based on these solutions, we study the temperature dependent condensation of dual operator of massive and massless scalar respectively. These condensations show that there might be phase transitions in deformed CFTs. We also compare free energy between hyperbolic black hole solutions and hyperbolic AdS-SW black hole to judge phase transitions. In order to confirm the existence of phase transitions, we turn on linear in-homogenous perturbation to test stability of these hyperbolic AdS black holes. In this paper, we show how potential parameters affect the stability of hy...
Entropy production, viscosity bounds and bumpy black holes
Hartnoll, Sean A; Santos, Jorge E
2016-01-01
The ratio of shear viscosity to entropy density, $\\eta/s$, is computed in various holographic geometries that break translation invariance (but are isotropic). The shear viscosity does not have a hydrodynamic interpretation in such backgrounds, but does quantify the rate of entropy production due to a strain. Fluctuations of the metric components $\\delta g_{xy}$ are massive about these backgrounds, leading to $\\eta/s < 1/(4\\pi)$ at all finite temperatures (even in Einstein gravity). As the temperature is taken to zero, different behaviors are possible. If translation symmetry breaking is irrelevant in the far IR, then $\\eta/s$ tends to a constant at $T=0$. This constant can be parametrically small. If the translation symmetry is broken in the far IR (which nonetheless develops emergent scale invariance), then $\\eta/s \\sim T^{2 \
The Thermodynamics of Black Holes
Directory of Open Access Journals (Sweden)
Wald Robert M.
2001-01-01
Full Text Available We review the present status of black hole thermodynamics. Our review includes discussion of classical black hole thermodynamics, Hawking radiation from black holes, the generalized second law, and the issue of entropy bounds. A brief survey also is given of approaches to the calculation of black hole entropy. We conclude with a discussion of some unresolved open issues.
International Nuclear Information System (INIS)
In this work we apply the generalized uncertainty principle (GUP) to the problem of maximum entropy and evaporation/absorption of the energy of black holes near the Planck scale. Within this general approach we find corrections to the maximum entropy and indications of the quenching of evaporation, not only because the evaporation term goes to a finite limit, but also because the absorption of quanta seems to help the balance for black holes in a thermal bath. Then, residual masses at around the Planck scale may be the final outcome of primordial black-hole evaporation. (letter to the editor)
Lan, Xiao-Gang
2013-05-01
By introducing a new tortoise coordinate transformation, we apply Damour-Ruffini-Sannan method to study the Hawking radiation of massive scalar particles in a dynamic Dilaton-Maxwell black hole. We find that Hawking radiation spectrum shows still the blackbody one, while the Hawking temperature is significantly changed. Additionally, by adopting the thin film method, we calculate the entropy of a dynamic Dilaton-Maxwell black hole. The result indicates that the entropy for such a black hole is still in proportional to the area of its event horizon.
Holographic entanglement entropy and the extended phase structure of STU black holes
Caceres, Elena; Pedraza, Juan F
2015-01-01
We study the extended thermodynamics, obtained by considering the cosmological constant as a thermodynamic variable, of STU black holes in 4-dimensions in the fixed charge ensemble. The associated phase structure is conjectured to be dual to an RG-flow on the space of field theories. We find that for some charge configurations the phase structure resembles that of a Van der Waals gas: the system exhibits a family of first order phase transitions ending in a second order phase transition at a critical temperature. We calculate the holographic entanglement entropy for several charge configurations and show that for the cases where the gravity background exhibits Van der Waals behavior, the entanglement entropy presents a transition at the same critical temperature. To further characterize the phase transition we calculate appropiate critical exponents show that they coincide. Thus, the holographic entanglement entropy successfully captures the information of the extended phase structure. Finally, we discuss the...
Near-Horizon Geometry and the Entropy of a Minimally Coupled Scalar Field in the Kerr Black Hole
Ghosh, Kaushik
2016-01-01
In this article we will discuss a Lorentzian sector calculation of the entropy of a minimally coupled scalar field in the Kerr black hole background. We will use the brick wall model of t' Hooft. In the Kerr black hole, complications arise due to the absence of a global timelike Killing field and the presence of the ergosphere. Nevertheless, it is possible to calculate the entropy of a thin shell of matter field in the near-horizon region using the brick wall model. The corresponding leading order entropy of the nonsuperradiant modes is found to be proportional to the area of the horizon and is logarithmically divergent. Thus, the entropy of a three dimensional system in the near-horizon region is proportional to the boundary surface. This is similar to that of the black hole entropy itself. The corresponding internal energy remains finite if the entropy is chosen to be of the order of the black hole entropy itself. The leading order entropy is found to be half of the corresponding term in the Schwarzschild b...
FORMATION OF BLACK HOLE AND ACCRETION DISK IN A MASSIVE HIGH-ENTROPY STELLAR CORE COLLAPSE
International Nuclear Information System (INIS)
We present the first numerical result of fully general relativistic axisymmetric simulations for the collapse of a rotating high-entropy stellar core to a black hole and an accretion disk. The simulations are performed taking into account the relevant microphysics. We adopt as initial conditions a spherical core with constant electron fraction (Ye = 0.5) and entropy per baryon s = 8 kB , and angular velocity is superimposed. In the early phase, the core collapses in a homologous manner. Then it experiences a weak bounce due to the gas pressure of free nucleons. Because the bounce is weak, the core eventually collapses to a black hole. Subsequent evolution depends on initial angular velocity. When the rotation is not fast, a geometrically thin (but optically thick) accretion disk is formed, and shock waves are formed in the inner part of the disk. For the moderately rotating case, the thin accretion disk eventually expands to become a geometrically thick torus after sufficient accumulation of the thermal energy is generated at the shocks. Furthermore, convection occurs inside the torus. Neutrino luminosities vary violently with time because of the convective motion. For the rapidly rotating case, by contrast, a geometrically thick torus is formed soon after the black hole formation, and the convective activity is weak due to the presence of an epicyclic mode.
Refined Holographic Entanglement Entropy for the AdS Solitons and AdS black Holes
Ishihara, Masafumi; Ning, Bo
2012-01-01
We consider the refinement of the holographic entanglement entropy on a disk region for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss-Bonnet term. The AdS soliton is dual to a gapped system with an IR fixed-point. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy. We then study the renormalization group (RG) flow of the refinement by tuning the linear size of the chosen disk region. Our main results are (i) the RG flow of the refinement decreases monotonically for most of the cases; (ii) there is no topological entanglement entropy for AdS$_5$ soliton even with Gauss-Bonnet correction; (iii) for the AdS black holes, the refinement obeys the volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover; however, the crossover will turn into phase transition by the Gauss-Bonnet correction; (iv) for the AdS solitons, there are discontinuous phase transitions bet...
Energy Technology Data Exchange (ETDEWEB)
Lopez-DomInguez, J C [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); RamIrez, C [Facultad de Ciencias FIsico Matematicas, Universidad Autonoma de Puebla, PO Box 1364, 72000 Puebla (Mexico); Sabido, M [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico)
2007-11-15
We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole.
Entropy of extremal black holes: horizon limits through charged thin shells, a unified approach
Lemos, José P S; Zaslavskii, Oleg B
2016-01-01
Using a unified approach we study the entropy of extremal black holes through the entropy of an electrically charged thin shell. We encounter three cases in which a shell can be taken to its own gravitational or horizon radius and become an extremal spacetime. In case 1, we use a non extremal shell, calculate all the thermodynamics quantities including the entropy, take it to the horizon radius, and then take the extremal limit. In case 2, we take the extremal limit and the horizon radius limit simultaneously, i.e., as the shell approaches its horizon radius it also approaches extremality. In case 3, we build first an extremal shell, and then take its horizon radius. We find that the thermodynamic quantities in general have different expressions in the three different cases. The entropy is the Bekenstein-Hawking entropy $ S=A_+/4$ (where $A_+$ is the horizon area) in cases 1 and 2, and in case 3 it can be any well-behaved function of $A_+$. The contributions from the various thermodynamic quantities for the e...
The black hole entropy bound and the maximum temperature for meson formation in the nuclear fireball
International Nuclear Information System (INIS)
The entropy bound from black hole thermodynamics can be invoked to set limits for temperatures at which hadrons can survive as a confined system. The authors find that this implies that the pion can be formed in heavy ion collisions; much later than heavier mesons, for example the p-meson, when the fireball is cooler. The temperature found in a simple model agree qualitatively with experiment. This paper suggests that this may be the reason why in pion interferometry experiments the space-time volume of the pion source seems large
Entropy of near-extremal black holes in AdS5
Balasubramanian, Vijay
2008-01-01
We construct the microstates of near-extremal black holes in AdS_5 x S5 as gases of defects distributed in heavy BPS operators in the dual SU(N) Yang-Mills theory. These defects describe open strings on spherical D3-branes in the S5, and we show that they dominate the entropy by directly enumerating them and comparing the results with a partition sum calculation. We display new decoupling limits in which the field theory of the lightest open strings on the D-branes becomes dual to a near-hori...
Wang, Jia; Meng, Xin-he
2014-01-01
We present a new universal property of entropy, that is the entropy sum relation of black holes in four dimensional (anti-)de-Sitter asymptotical back- ground. They depend only on the cosmological constant with the necessary e?ect of the un-physical virtual horizon included in the spacetime where only the cosmological constant, mass of black hole, rotation parameter and Maxwell ?eld exist. When there is more extra matter ?eld in the spacetime, one will ?nd the entropy sum is also dependent of the strength of these extra matter ?eld. For both cases, we conclude that the entropy sum does not depend on the con- versed charges M, Q and J, while it does depend on the property of background spacetime. We will mainly test the entropy sum relation in static, stationary black hole and some black hole with extra matter source (scalar hair and higher curvature) in the asymptotical (anti-)de-sitter spacetime background. Besides, we point out a newly found counter example of the mass independence of the "entropy product" ...
Exact holography and black hole entropy in N=8 and N=4 string theory
Gomes, Joao
2015-01-01
We compute the exact entropy of one-eighth and one-quarter BPS black holes in N=8 and N=4 string theory respectively. This includes all the N=4 CHL models in both K3 and T^4 compactifications. The main result is a measure for the finite dimensional integral that one obtains after localization of supergravity on AdS_2xS^2. This measure is determined entirely by an anomaly in supersymmetric Chern-Simons theory on local AdS_3 and takes into account the contribution from all the supergravity multiplets. In Chern-Simons theory on compact manifolds this is the anomaly that computes a certain one-loop dependence on the volume of the manifold. For one-eighth BPS black holes our results are a first principles derivation of a measure proposed in arXiv:1111.1161, while in the case of one-quarter BPS black holes our result computes exactly all the perturbative or area corrections. Moreover, we argue that instantonic contributions can be incorporated and give evidence by computing the measure which matches precisely the m...
Liang, Jun
2014-01-01
By employing an adiabatic invariant and implementing the Bohr-Sommerfield quantization rule, I study the quantization of a regular black hole inspired by noncommutative geometry in AdS3 spacetime. The entropy spectrum as well as the horizon area spectrum of the black hole is obtained. It is shown that the spectra are discrete, and the spacing of the entropy spectrum is equidistant; in the limit , the area spectrum depends on the noncommutative parameter and the cosmological constant, but the spacing of the area spectrum is equidistant up to leading order in θ, and is independent of the noncommutative parameter and the cosmological constant.
Directory of Open Access Journals (Sweden)
Wei Xu
2015-03-01
Full Text Available Based on entropy relations, we derive the thermodynamic bound for entropy and the area of horizons for a Schwarzschild–dS black hole, including the event horizon, Cauchy horizon, and negative horizon (i.e., the horizon with negative value, which are all geometrically bound and comprised by the cosmological radius. We consider the first derivative of the entropy relations to obtain the first law of thermodynamics for all horizons. We also obtain the Smarr relation for the horizons using the scaling discussion. For the thermodynamics of all horizons, the cosmological constant is treated as a thermodynamic variable. In particular, the thermodynamics of the negative horizon are defined well in the r<0 side of space–time. This formula appears to be valid for three-horizon black holes. We also generalize the discussion to thermodynamics for the event horizon and Cauchy horizon of Gauss–Bonnet charged flat black holes because the Gauss–Bonnet coupling constant is also considered to be thermodynamic variable. These results provide further insights into the crucial role played by the entropy relations of multi-horizons in black hole thermodynamics as well as improving our understanding of entropy at the microscopic level.
On Noncommutative Black Holes Thermodynamics
Faizal, Mir; Ulhoa, S C
2015-01-01
In this paper, we will analyze noncommutative deformation of the Schwarzschild black holes and Kerr black holes. We will perform our analysis by relating the commutative and the noncommutative metrics using an Moyal product. We will also analyze the thermodynamics of these noncommutative black hole solutions. We will explicitly derive expression for the corrected entropy and temperature of these black hole solutions.
El-Menoufi, Basem Kamal
2016-05-01
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
Energy Technology Data Exchange (ETDEWEB)
Ferreiro Perez, Roberto, E-mail: roferreiro@ccee.ucm.e [Departamento de Economia Financiera y Contabilidad I Facultad de Ciencias Economicas y Empresariales, UCM Campus de Somosaguas, 28223-Pozuelo de Alarcon (Spain)
2010-07-07
The Chern-Simons Lagrangian density in the space of metrics of a three-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the Lagrangian is not invariant, the Noether theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a Hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.
Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings
Bonelli, G
2007-01-01
We study cohomological gauge theories on total spaces of holomorphic line bundles over complex manifolds and obtain their reduction to the base manifold by U(1) equivariant localization of the path integral. We exemplify this general mechanism by proving via exact path integral localization a reduction for local curves conjectured in hep-th/0411280, relevant to the calculation of black hole entropy/Gromov-Witten invariants. Agreement with the four-dimensional gauge theory is recovered by taking into account in the latter non-trivial contributions coming from one-loop fluctuations determinants at the boundary of the total space. We also study a class of abelian gauge theories on Calabi-Yau local surfaces, describing the quantum foam for the A-model, relevant to the calculation of Donaldson-Thomas invariants.
Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
International Nuclear Information System (INIS)
The Chern-Simons Lagrangian density in the space of metrics of a three-dimensional manifold M is not invariant under the action of diffeomorphisms on M. However, its Euler-Lagrange operator can be identified with the Cotton tensor, which is invariant under diffeomorphims. As the Lagrangian is not invariant, the Noether theorem cannot be applied to obtain conserved currents. We show that it is possible to obtain an equivariant conserved current for the Cotton tensor by using the first equivariant Pontryagin form on the bundle of metrics. Finally we define a Hamiltonian current which gives the contribution of the Chern-Simons term to the black hole entropy, energy and angular momentum.
Quasinormal modes of charged dilaton black holes and their entropy spectra
Sakalli, I
2013-01-01
In this study, we employ the scalar perturbations of the charged dilaton black hole (CDBH) found by Chan, Horne and Mann (CHM), and described with an action which emerges in the low-energy limit of the string theory. A CDBH is neither asymptotically flat (AF) nor non-asymptotically flat (NAF) spacetime. Depending on the value of its dilaton parameter "a", it has both Schwarzschild and linear dilaton black hole (LDBH) limits. We compute the complex frequencies of the quasinormal modes (QNM) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNMs in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these BHs. Although the QNM frequencies are tuned by "a", we show that the quantum spectra do not depend on "a", and they are equally spaced. On the other hand, the obtained value of undetermined dimensionless constant {\\epsilon} is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.
Luminet, Jean-Pierre
1992-09-01
Foreword to the French edition; Foreword to the English edition; Acknowledgements; Part I. Gravitation and Light: 1. First fruits; 2. Relativity; 3. Curved space-time; Part II. Exquisite Corpses: 4. Chronicle of the twilight years; 5. Ashes and diamonds; 6. Supernovae; 7. Pulsars; 8. Gravitation triumphant; Part III. Light Assassinated: 9. The far horizon; 10. Illuminations; 11. A descent into the maelstrom; 12. Map games; 13. The black hole machine; 14. The quantum black hole; Part IV. Light Regained: 15. Primordial black holes; 16. The zoo of X-ray stars; 17. Giant black holes; 18. Gravitational light; 19. The black hole Universe; Appendices; Bibliography; Name index; Subject index.
Institute of Scientific and Technical Information of China (English)
CHEN Qiang; REN Ji-Rong
2013-01-01
In this paper,we use the modified Hod's treatment and the Kunstatter's method to study the horizon area spectrum and entropy spectrum in Gauss-Bonnet de-Sitter space-time,which is regarded as the natural generalization of Einstein gravity by including higher derivative correction terms to the original Einstein-Hilbert action.The horizon areas have some properties that are very different from the vacuum solutions obtained from the frame of Einstein gravity.With the new physical interpretation of quasinormal modes,the area/entropy spectrum for the event horizon for nearextremal Gauss-Bonnet de Sitter black holes are obtained.Meanwhile,we also extend the discussion of area/entropy quantization to the non-extremal black holes solutions.
International Nuclear Information System (INIS)
In this paper, we use the modified Hod's treatment and the Kunstatter's method to study the horizon area spectrum and entropy spectrum in Gauss—Bonnet de-Sitter space-time, which is regarded as the natural generalization of Einstein gravity by including higher derivative correction terms to the original Einstein—Hilbert action. The horizon areas have some properties that are very different from the vacuum solutions obtained from the frame of Einstein gravity. With the new physical interpretation of quasinormal modes, the area/entropy spectrum for the event horizon for near-extremal Gauss—Bonnet de Sitter black holes are obtained. Meanwhile, we also extend the discussion of area/entropy quantization to the non-extremal black holes solutions. (general)
More on area density of localization-entropy and problematization of black hole entropy
Schrör, B
2005-01-01
The holographic boundary projection method for the study of vacuum-polarization caused thermal aspects is extended to double cone localized algebras. As in the previous case of wedge algebras, this algebra in its restricted vacuum state is identical to its holographic projection onto its causal horizon and can be approximated from the inside in analogy to the thermodynamic limit approximation. The spectrum of the modular ``Hamiltonian'' of each approximand is discrete and converges against the desired continuous modular Hamiltonian. In the correspondence to the standard thermodynamic limit two of the length dimensions of the volume factor correspond to the transverse extension (the area factor $l^{2}$) of the holographic projection and the remaining third dimension passes to the inverse of the lightlike distance $\\epsilon $ of the approximand from its limit; hence altogether the localization entropy behaves as $l^{2}\\times \\frac{1}{\\epsilon}$ with the proportionality constant being determined by the holograph...
Tanaka, Sho
2014-01-01
In confrontation with serious and fundamental problems towards ultimate theory of quantum gravity and Planck scale physics, we emphasize the importance of underlying noncommutative space-time such as Snyder's or Yang's Lorentz-covariant quantized space-time. The background of Bekenstein-Hawking's area-entropy law and holographic principle is now substantially understood in terms of Kinematical Holographic Relation (KHR), which holds in Yang's quantized space-time as the result of the kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry. KHR implies a proportional relation, , between the number of spatial degrees of freedom inside any d -dimensional spherical volume with radius L and its boundary area . It yields a substantial basis for our new area-entropy law of black holes and further enables us to connect "the first law of black hole mechanics" with "the thermodynamics of black holes" towards our final goal: A statistical and substantial understanding of the area-entropy law of black holes under a novel concept of noncommutative quantized space-time.
Bak, Dongsu; Gutperle, Michael; Janik, Romuald A.
2011-10-01
In this paper Janus black holes in A dS 3 are considered. These are static solutions of an Einstein-scalar system with broken translation symmetry along the horizon. These solutions are dual to interface conformal field theories at finite temperature. An approximate solution is first constructed using perturbation theory around a planar BTZ blackhole. Numerical and exact solutions valid for all sets of parameters are then found and compared. Using the exact solution the thermodynamics of the system is analyzed. The entropy associated with the Janus black hole is calculated and it is found that the entropy of the black Janus is the sum of the undeformed black hole entropy and the entanglement entropy associated with the defect.
Institute of Scientific and Technical Information of China (English)
XU Dian-Yan
2003-01-01
The free energy and entropy of Reissner-Nordstrom black holes in higher-dimensional space-time are calculated by the quantum statistic method with a brick wall model. The space-time of the black holes is divided into three regions: region 1, (r > r0); region 2, (r0 > r > n); and region 3, (T-J > r > 0), where r0 is the radius of the outer event horizon, and r, is the radius of the inner event horizon. Detailed calculation shows that the entropy contributed by region 2 is zero, the entropy contributed by region 1 is positive and proportional to the outer event horizon area, the entropy contributed by region 3 is negative and proportional to the inner event horizon area. The total entropy contributed by all the three regions is positive and proportional to the area difference between the outer and inner event horizons. As rt approaches r0 in the nearly extreme case, the total quantum statistical entropy approaches zero.
Energy Technology Data Exchange (ETDEWEB)
Myung, Y.S
2003-11-13
We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing k by -k. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences.
Myung, Y S
2003-01-01
We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing $k$ by $-k$. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences.
Directory of Open Access Journals (Sweden)
M.R. Setare
2016-01-01
Full Text Available In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern–Simons-like theories of gravity (CSLTG and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
Setare, M R
2016-01-01
In the first order formalism of gravity theories, may be exist some theories which are not Lorentz-difeomorphism covariant so for such theories a method for which one can calculate conserved charges of Lorentz-difeomorphism covariant theories are useless. In this letter we introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Then using this concept, in order to obtain the conserved charges in Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa's method \\cite{3} so that it includes Lorentz gauge transformation in addition to diffeomorphism. We apply this method on the Chern-Simons-like theories of gravity and we find out a general formula for the entropy of black holes in those theories. Eventually, we consider some examples and calculate entropy of the BTZ black hole in the context of this examples.
Setare, M. R.; Adami, H.
2016-01-01
In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern-Simons-like theories of gravity (CSLTG) and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
International Nuclear Information System (INIS)
By employing an adiabatic invariant and implementing the Bohr-Sommerfield quantization rule, I study the quantization of a regular black hole inspired by noncommutative geometry in AdS3 spacetime. The entropy spectrum as well as the horizon area spectrum of the black hole is obtained. It is shown that the spectra are discrete, and the spacing of the entropy spectrum is equidistant; in the limit (rh2)/4θ >> 1, the area spectrum depends on the noncommutative parameter and the cosmological constant, but the spacing of the area spectrum is equidistant up to leading order √θe-(2Ml2)/θ in θ, and is independent of the noncommutative parameter and the cosmological constant. (research papers)
Directory of Open Access Journals (Sweden)
Sergio Mendoza
2009-01-01
Full Text Available We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than Rs, in the vicinity of Rs. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent Ã¢Â€Â™particleÃ¢Â€Â™ description fails, and the wave nature becomes apparent.
Revisit emission spectrum and entropy quantum of the Reissner-Nordstr\\"{o}m black hole
Jiang, Qing-Quan
2012-01-01
Banerjee and Majhi's recent work shows that black hole's emission spectrum could be fully reproduced in the tunneling picture, where, as an intriguing technique, the Kruskal extension was introduced to connect the left and right modes inside and outside the horizon. Some attempt, as an extension, was focused on producing the Hawking emission spectrum of the (charged) Reissner-Nordstr\\"{o}m black hole in the Banerjee-Majhi's treatment. Unfortunately, the Kruskal extension in their observation was so badly defined that the ingoing mode was classically forbidden traveling towards the center of black hole, but could quantum tunnel across the horizon with the probability $\\Gamma=e^{-\\pi \\omega_0/\\kappa_+}$. This tunneling picture is unphysical. With this point as a central motivation, in this paper we first introduce such a suitable Kruskal extension for the (charged) Reissner-Nordstr\\"{o}m black hole that a perfect tunneling picture can be provided during the charged particle's emission. Then, under the new Krusk...
(Anti-)de Sitter Black Hole Entropy and Generalized Uncertainty Principle
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Li-Chun; HU Shuang-Qi
2006-01-01
We generalize the method that is used to study corrections to Cardy-Verlinde formula due to generalized uncertainty principle and discuss corrections to Cardy-Verlinde formula due to generalized uncertainty principle in (anti)-de Sitter space. Because in de Sitter black hole spacetime the radiation temperature of the black hole horizon is different from the one of the cosmological horizon, this spacetime is a thermodynamical non-equilibrium spacetime.
Towards noncommutative quantum black holes
International Nuclear Information System (INIS)
In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawking's temperature and entropy for the noncommutative Schwarzschild black hole
Towards Noncommutative Quantum Black Holes
Lopez-Dominguez, J. C.; Obregon, O.; Ramirez, C.; Sabido, M.
2006-01-01
In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawking's temperature and entropy for the noncommutative Schwarzschild black hole.
Fluctuating Black Hole Horizons
Mei, Jianwei
2013-01-01
In this paper we treat the black hole horizon as a physical boundary to the spacetime and study its dynamics following from the Gibbons-Hawking-York boundary term. Using the Kerr black hole as an example we derive an effective action that describes, in the large wave number limit, a massless Klein-Gordon field living on the average location of the boundary. Complete solutions can be found in the small rotation limit of the black hole. The formulation suggests that the boundary can be treated in the same way as any other matter contributions. In particular, the angular momentum of the boundary matches exactly with that of the black hole, suggesting an interesting possibility that all charges (including the entropy) of the black hole are carried by the boundary. Using this as input, we derive predictions on the Planck scale properties of the boundary.
Bena, Iosif; Chowdhury, Borun D.; de Boer, Jan; El-Showk, Sheer; Shigemori, Masaki
2012-03-01
We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of charges have more entropy than all known ensembles. We also find bulk BPS configurations that exist in the same range of parameters as these phases, and have more entropy than a BMPV black hole; they can be thought of as coming from a BMPV black hole shedding a "hair" condensate outside of the horizon. The entropy of the bulk configurations is smaller than that of the CFT phases, which indicates that some of the CFT states are lifted at strong coupling. Neither the bulk nor the boundary phases are captured by the elliptic genus, which makes the coincidence of the phase boundaries particularly remarkable. Our configurations are supersymmetric, have non-Cardy-like entropy, and are the first instance of a black hole entropy enigma with a controlled CFT dual. Furthermore, contrary to common lore, these objects exist in a region of parameter space (between the "cosmic censorship bound" and the "unitarity bound") where no black holes were thought to exist.
Supersymmetric black holes in string theory
Mohaupt, T.
2007-01-01
We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2 supergravity, special geometry, the black hole attractor equations and the underlying variational principle. Special attention is payed to the crucial role of higher derivative corrections. Finally we discuss black hole partition functions and their relation to t...
Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
Gupta, Kumar; Harikumar, E.; Jurić, Tajron; Meljanac, Stjepan; Samsarov, Andjelo
2015-01-01
We obtain an exact analytic expression for the quasinormal modes of a non-commutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutat...
Brown, J D; York, James W.
1993-01-01
The authors have recently proposed a "microcanonical functional integral" representation of the density of quantum states of the gravitational field. The phase of this real-time functional integral is determined by a "microcanonical" or Jacobi action, the extrema of which are classical solutions at fixed total energy, not at fixed total time interval as in Hamilton's action. This approach is fully general but is especially well suited to gravitating systems because for them the total energy can be fixed simply as a boundary condition on the gravitational field. In this paper we describe how to obtain Jacobi's action for general relativity. We evaluate it for a certain complex metric associated with a rotating black hole and discuss the relation of the result to the density of states and to the entropy of the black hole.
Hernández, X; Mendoza, S; Sussman, R A
2005-01-01
We study the relationship between the energy and entropy of a black body photon gas, within an idealised spherical adiabatic enclosure of radius R, as this is compressed into a self-gravitating regime. We show that this regime approximately coincides with the black hole regime for the system, i.e., R ~ R_{s}, where R_{s} denotes the Schwarzschild radius of the system. The entropy of this system is always below the suggested Holographic bound, even as R \\to R_{s}. A plausible quantum configuration for the photon gas at R \\to R_{s} is suggested, which satisfies all energy, entropy and temperature black hole conditions. Finally we examine our results from the point of view of recent Loop Quantum Gravity ideas.
Chrúsciel, P T
2002-01-01
This paper is concerned with several not-quantum aspects of black holes, with emphasis on theoretical and mathematical issues related to numerical modeling of black hole space-times. Part of the material has a review character, but some new results or proposals are also presented. We review the experimental evidence for existence of black holes. We propose a definition of black hole region for any theory governed by a symmetric hyperbolic system of equations. Our definition reproduces the usual one for gravity, and leads to the one associated with the Unruh metric in the case of Euler equations. We review the global conditions which have been used in the Scri-based definition of a black hole and point out the deficiencies of the Scri approach. Various results on the structure of horizons and apparent horizons are presented, and a new proof of semi-convexity of horizons based on a variational principle is given. Recent results on the classification of stationary singularity-free vacuum solutions are reviewed. ...
Radiation spectrum of rotating Gdel black hole and correction entropy
Institute of Scientific and Technical Information of China (English)
张丽春; 林海; 李怀繁; 赵仁
2011-01-01
We study the Hawking radiation of the scalar field in the rotating Gdel black hole in minimal five-dimensional supergravity. We not only derive radiation spectra that satisfy the unitary principle but also obtain the correction term of Bekenstein-Hawking
Towards a Theory of Quantum Black Hole
Berezin, V.
2001-01-01
We describe some specific quantum black hole model. It is pointed out that the origin of a black hole entropy is the very process of quantum gravitational collapse. The quantum black hole mass spectrum is extracted from the mass spectrum of the gravitating source. The classical analog of quantum black hole is constructed.
Ordonez, Carlos
2010-10-01
A review and the latest results on the near-horizon expansion (conformal) approach to `t Hooft's brick-wall model calculation of Black Hole entropy developed recently by the speaker and his collaborators will be given in this talk. With mainly a graduate student audience in mind, the seminar will be pedagogical in nature, with emphasis on the ideas and logic of the methods and the insights gained with this approach more than on details. If time permits, possible future directions will also be mentioned.
Vaz, Cenalo; Wijewardhana, L. C. R.
2013-12-01
General consensus on the nature of the degrees of freedom responsible for the black hole entropy remains elusive despite decades of effort dedicated to the problem. Different approaches to quantum gravity disagree in their description of the microstates and, more significantly, in the statistics used to count them. In some approaches (string theory, AdS/CFT) the elementary degrees of freedom are indistinguishable, whereas they must be treated as distinguishable in other approaches to quantum gravity (eg., LQG) in order to recover the Bekenstein-Hawking area-entropy law. However, different statistics will imply different behaviors of the black hole outside the thermodynamic limit. We illustrate this point by quantizing the Bañados-Teitelboim-Zanelli (BTZ) black hole, for which we argue that Bose condensation will occur leading to a "cold", stable remnant.
International Nuclear Information System (INIS)
's research councils have yet to put any real money behind these ideas. Black holes are best described by the general theory of relativity. However, general relativity is a classical theory of gravity, and although its predictions have been verified in many experiments, a quantum theory of gravity remains one of the holy grails of physics. One of the first physicists to make real progress in this quest to reconcile general relativity and quantum mechanics was Stephen Hawking. In 1974 Hawking calculated what would happen if a quantum fluctuation occurred near an event horizon. He concluded that the black hole would radiate, and that the amount of radiation would be inversely proportional to the mass of the black hole. However, black holes tend to be very heavy, so their output of Hawking radiation would be too low to detect experimentally. One intriguing exception could be much smaller primordial black holes created in the big bang: these should radiate observable amounts of gamma rays, but they have not been detected yet. This whole body of work - in which thermodynamic concepts such as temperature and entropy are also associated with the black hole - is Hawking's major achievement in physics. The detection of Hawking radiation is the ultimate goal of experiments on artificial black holes, although a lot of theoretical and experimental work has to be done first. The successful experiment is likely to involve a flowing Bose-Einstein condensate or a medium in which the speed of light can be reduced to zero. After years of groundwork, physicists have recently made rapid progress in both these fields. Meanwhile, the recent observation of neutrons in discrete quantum states in a gravitational potential shows that quantum gravity effects can be seen in the laboratory. All that is needed now is an act of faith. (U.K.)
Corda, C; Katebi, R; Schmidt, N O
2014-01-01
Black hole (BH) quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In this specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and non-strictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, this work exemplifies a series of imperative corrections that eventually permits a BH's horizon area spectrum to be generalized from strictly thermal to non-strictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the identified results are significant because quasi-normal modes (QNM) and "effective ...
Bena, Iosif; de Boer, Jan; El-Showk, Sheer; Shigemori, Masaki
2011-01-01
We find a family of novel supersymmetric phases of the D1-D5 CFT, which in certain ranges of charges have more entropy than all known ensembles. We also find bulk BPS configurations that exist in the same range of parameters as these phases, and have more entropy than a BMPV black hole; they can be thought of as coming from a BMPV black hole shedding a "hair" condensate outside of the horizon. The entropy of the bulk configurations is smaller than that of the CFT phases, which indicates that some of the CFT states are lifted at strong coupling. Neither the bulk nor the boundary phases are captured by the elliptic genus, which makes the coincidence of the phase boundaries particularly remarkable. Our configurations are supersymmetric, have non-Cardy-like entropy, and are the first instance of a black hole entropy enigma with a controlled CFT dual. Furthermore, contrary to common lore, these objects exist in a region of parameter space (between the "cosmic censorship bound" and the "unitarity bound") where no b...
Phase transition and entropy inequality of noncommutative black holes in a new extended phase space
Miao, Yan-Gang; Xu, Zhen-Ming
2016-01-01
We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as {\\em the noncommutative pressure}. In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative co...
Liu, Molin
2011-01-01
Motivated by recent logarithmic entropy of Ho$\\check{r}$ava-Lifshitz gravity, we investigate Hawking radiation for Kehagias-Sfetsos black hole from tunneling perspective. After considering the effect of self-gravitation, we calculate the emission rate and entropy of quantum tunneling by using Kraus-Parikh-Wilczek method. Meanwhile, both massless and massive particles are considered in this letter. Interestingly, two types tunneling particles have the same emission rate $\\Gamma$ and entropy $S_b$ whose analytical formulae are $\\Gamma = \\exp{[\\pi (r_{in}^2 - r_{out}^2t)/2 + \\pi/\\alpha \\ln r_{in}/r_{out}]}$ and $S_b = A/4 + \\pi/\\alpha \\ln (A/4)$, respectively. Here, $\\alpha$ is the Ho$\\check{r}$ava-Lifshitz field parameter. The results show that the logarithmic entropy of Ho$\\check{r}$ava-Lifshitz gravity could be explained well by the self-gravitation, which is totally different from other methods. The study of this semiclassical tunneling process may shed light on the understand of Ho$\\check{r}$ava-Lifshitz gr...
Regular black hole in three dimensions
Myung, Yun Soo; Yoon, Myungseok
2008-01-01
We find a new black hole in three dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare thermodynamics of this black hole with that of non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein-Hawking entropy.
Regular black hole in three dimensions
International Nuclear Information System (INIS)
We find a new black hole in three-dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare the thermodynamics of this black hole with that of a non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein-Hawking entropy. (orig.)
Regular black hole in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Myung, Yun Soo [Inje University, Institute of Basic Science and School of Computer Aided Science, Gimhae (Korea); Yoon, Myungseok [Sogang University, Center for Quantum Spacetime, Seoul (Korea)
2009-07-15
We find a new black hole in three-dimensional anti-de Sitter space by introducing an anisotropic perfect fluid inspired by the noncommutative black hole. This is a regular black hole with two horizons. We compare the thermodynamics of this black hole with that of a non-rotating BTZ black hole. The first-law of thermodynamics is not compatible with the Bekenstein-Hawking entropy. (orig.)
International Nuclear Information System (INIS)
We present a new “universal property” of entropy, that is the “entropy sum” relation of black holes in four dimensional (anti-)de-Sitter asymptotical background. They depend only on the cosmological constant with the necessary effect of the un-physical “virtual” horizon included in the spacetime where only the cosmological constant, mass of black hole, rotation parameter and Maxwell field exist. When there is more extra matter field in the spacetime, one will find the “entropy sum” is also dependent of the strength of these extra matter field. For both cases, we conclude that the “entropy sum” does not depend on the conserved charges M, Q and J, while it does depend on the property of background spacetime. We will mainly test the “entropy sum” relation in static, stationary black hole and some black hole with extra matter source (scalar hair and higher curvature) in the asymptotical (anti-)de-sitter spacetime background. Besides, we point out a newly found counter example of the mass independence of the ”entropy product” relation in the spacetime with extra scalar hair case, while the “entropy sum” relation still holds. These result are indeed suggestive to some underlying microscopic mechanism. Moreover, the cosmological constant and extra matter field dependence of the “entropy sum” of all horizon seems to reveal that “entropy sum” is more general as it is only related to the background field. For the case of asymptotical flat spacetime without any matter source, we give a note for the Kerr black hole case in appendix. One will find only mass dependence of “entropy sum” appears. It makes us believe that, considering the dependence of “entropy sum”, the mass background field may be regarded as the next order of cosmological constant background field and extra matter field. However, fully explaining the relationship between the “entropy sum” relation and background properties still requires further exploration
Tanaka, Sho
2014-01-01
In confrontation with serious and fundamental problems towards ultimate theory of quantum gravity and physics of Planck scale, we emphasize the importance of underlying noncommutative space-time such as Snyder's or Yang's Lorentz-covariant quantized space-time. The background of Bekenstein-Hawking's Area-entropy law and Holographic principle is now substantially understood in terms of {\\it Kinematical} Holographic Relation [KHR], which holds in Yang's quantized space-time as the result of the kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry. [KHR] implies a definite proportional relation, $ n^L_{\\rm dof} (V_d^L)= {\\cal A} (V_d^L) / G_d$, between the number of spatial degrees of freedom $n^L_{\\rm dof} (V_d^L)$ inside of any $d-$dimensional spherical volume $V_d^L$ with radius $L $ and its boundary area ${\\cal A} (V_d^L).$ It provides a substantial basis for our new area-entropy law of black hole and further enables us to connect "The First Law of Black Hol...
Thermodynamics of Accelerating Black Holes
Appels, Michael; Kubiznak, David
2016-01-01
We address a long-standing problem of describing the thermodynamics of a charged accelerating black hole. We derive a standard first law of black hole thermodynamics, with the usual identification of entropy proportional to the area of the event horizon -- even though the event horizon contains a conical singularity. This result not only extends the applicability of black hole thermodynamics to realms previously not anticipated, it also opens a possibility for studying novel properties of an important class of exact radiative solutions of Einstein equations describing accelerated objects. We discuss the thermodynamic volume, stability and phase structure of these black holes.
Noncommutative black hole thermodynamics
International Nuclear Information System (INIS)
We give a general derivation, for any static spherically symmetric metric, of the relation Th=(K/2π) connecting the black hole temperature (Th) with the surface gravity (K), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi-classical regime, i.e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space-time. The effects of backreaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and backreaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one
Thermodynamics of Horava-Lifshitz black holes
Energy Technology Data Exchange (ETDEWEB)
Myung, Yun Soo; Kim, Yong-Wan [Inje University, Institute of Basic Science and School of Computer Aided Science, Gimhae (Korea)
2010-07-15
We study black holes in the Horava-Lifshitz gravity with a parameter {lambda}. For 1/3{<=}{lambda}<3, the black holes behave the Lifshitz black holes with dynamical exponent 0
Bastos, C; Dias, N C; Prata, J N
2010-01-01
One considers phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model to study the interior of a Schwarzschild black hole. It is shown that the potential function of the corresponding quantum cosmology problem has a local minimum. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity regime and it is shown that the wave function vanishes in this limit.
Asin, Olivier; Geiller, Marc; Noui, Karim; Perez, Alejandro
2014-01-01
We study the thermodynamical properties of black holes when described as gases of indistinguishable punctures with a chemical potential. In this picture, which arises from loop quantum gravity, the black hole microstates are defined by finite families of half-integers spins coloring the punctures, and the near-horizon energy measured by quasi-local stationary observers defines the various thermodynamical ensembles. The punctures carry excitations of quantum geometry in the form of quanta of area, and the total horizon area $a_\\text{H}$ is given by the sum of these microscopic contributions. We assume here that the system satisfies the Bose-Einstein statistics, and that each microstate is degenerate with a holographic degeneracy given by $\\exp\\big(\\lambda a_\\text{H}/\\ell_\\text{Pl}^2\\big)$ and $\\lambda>0$. We analyze in detail the thermodynamical properties resulting from these inputs, and in particular compute the grand canonical entropy. We explain why the requirements that the temperature be fixed to the Unr...
Hidden Structures of Black Holes
Vercnocke, Bert
2010-01-01
This thesis investigates two main topics concerning black holes in extensions of general relativity inspired by string theory. First, the structure of the equations of motion underlying black hole solutions is considered, in theories of D-dimensional gravity coupled to scalars and vectors. For solutions preserving supersymmetry, the equations of motion have a dramatic simplification: they become first-order instead of the second-order equations one would expect. Recently, it was found that this is a feature some non-supersymmetric black hole solutions exhibit as well. We investigate if this holds more generally, by examining what the conditions are to have first-order equations for the scalar fields of non-supersymmetric black holes, that mimic the form of their supersymmetric counterparts. This is illustrated in examples. Second, the structure of black holes themselves is investigated. String theory has been successful in explaining the Bekenstein-Hawking entropy for (mainly supersymmetric) black holes from ...
STATISTICAL-MECHANICAL ENTROPY OF THE GENERAL STATIC BLACK HOLE DUE TO ELECTROMAGNETIC FIELD
Institute of Scientific and Technical Information of China (English)
JING JI-LIANG; YAN MU-LIN
2000-01-01
Statistical-mechanical entropy arising from the electromagnetic field in the general four-dimensional static blackhole spacetime is investigated by means of the "brick wall" model. An expression for the entropy is obtained and some examples are considered. The results show that the entropy arising from the electromagnetic field is exactly twice the one for a massless scalar field.
Extremal black holes in N=2 supergravity
Katmadas, S.
2011-01-01
An explanation for the entropy of black holes has been an outstanding problem in recent decades. A special case where this is possible is that of extremal black holes in N=2 supergravity in four and five dimensions. The best developed case is for black holes preserving some supersymmetry (BPS), whic
Can Black Hole Relax Unitarily?
Solodukhin, S N
2004-01-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.
Can Black Hole Relax Unitarily?
Solodukhin, S. N.
2005-03-01
We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.
International Nuclear Information System (INIS)
Black hole (BH) area quantization may be the key to unlocking a unifying theory of quantum gravity (QG). Surmounting evidence in the field of BH research continues to support a horizon (surface) area with a discrete and uniformly spaced spectrum, but there is still no general agreement on the level spacing. In the specialized and important BH case study, our objective is to report and examine the pertinent groundbreaking work of the strictly thermal and nonstrictly thermal spectrum level spacing of the BH horizon area quantization with included entropy calculations, which aims to tackle this gigantic problem. In particular, such work exemplifies a series of imperative corrections that eventually permits a BH’s horizon area spectrum to be generalized from strictly thermal to nonstrictly thermal with entropy results, thereby capturing multiple preceding developments by launching an effective unification between them. Moreover, the results are significant because quasi-normal modes (QNM) and “effective states” characterize the transitions between the established levels of the nonstrictly thermal spectrum
Voros product and noncommutative inspired black holes
Gangopadhyay, Sunandan
2013-01-01
We emphasize the importance of the Voros product in defining noncommutative inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordstr\\"{o}m black holes show that the area law holds upto order $\\frac{1}{\\sqrt{\\theta}}e^{-M^2/\\theta}$. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy $E$ for these black holes is then obtained and a deviation from the standard id...
Finite entropy of Schwarzschild anti-de Sitter black hole in different coordinates
Institute of Scientific and Technical Information of China (English)
Ding Chi-Kun; Jing Ji-Liang
2007-01-01
This paper studies the finite statistical-mechanical entropy of the Schwarzschild anti-de Sitter (AdS) spacetime At first glance, it seems that the results would be different from that in the Schwarzschild-like coordinate since both the entropies in these coordinates are exactly equivalent to that in the Schwarzschild-like coordinate.
Enthalpy, Geometric Volume and Logarithmic correction to Entropy for Van-der-Waals Black Hole
Pradhan, Parthapratim
2016-01-01
If the negative cosmological constant is treated as a dynamical pressure and if the volume be its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy. Under these circumstances, a new phenomena emerges in the context of extended phase space thermodynamics. We \\emph{examine} here these features for recently discovered Van-der-Waal (VDW) black hole (BH) \\cite{mann15} which is analogous to the VDW fluid. We show that the thermodynamic volume is \\emph{greater} than the naive geometric volume. We also show that the \\emph{Smarr-Gibbs-Duhem} relation is satisfied for this BH. Furthermore, by computing the thermal specific heat we find the local thermodynamic stability criterion for this BH. It has been observed that the BH does \\emph{not} possess any kind of second order phase transition. This is an interesting feature of VDW BH by its own right. Moreover, we also derive \\emph{Cosmic-Censorship-Inequality} for this class of BH. ...
Modified dispersion relations and black hole physics
Ling, Yi; Hu, Bo; Li, Xiang
2005-01-01
A modified formulation of energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such modification will give corrections to both the temperature and the entropy of black holes. In particular this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaching the Planck scale. It can prevent black holes from total evaporation, as a result pr...
Implementing black hole as efficient power plant
Wei, Shao-Wen; Liu, Yu-Xiao
2016-01-01
Treating the black hole molecules as working substance and considering its phase structure, we study the black hole heat engine by a charged anti-de Sitter black hole. In the reduced temperature-entropy chart, it is found that the work, heat, and efficiency of the engine are independent of the black hole charge. Applying the Rankine cycle with or without a back pressure mechanism to the black hole heat engine, the efficiency is numerically solved. The result shows that the black hole engine w...
Entanglement entropy and mutual information production rates in acoustic black holes.
Giovanazzi, Stefano
2011-01-01
A method to investigate acoustic Hawking radiation is proposed, where entanglement entropy and mutual information are measured from the fluctuations of the number of particles. The rate of entropy radiated per one-dimensional (1D) channel is given by S=κ/12, where κ is the sound acceleration on the sonic horizon. This entropy production is accompanied by a corresponding formation of mutual information to ensure the overall conservation of information. The predictions are confirmed using an ab initio analytical approach in transonic flows of 1D degenerate ideal Fermi fluids. PMID:21231730
Thermal corpuscular black holes
Casadio, Roberto; Giugno, Andrea; Orlandi, Alessio
2015-06-01
We study the corpuscular model of an evaporating black hole consisting of a specific quantum state for a large number N of self-confined bosons. The single-particle spectrum contains a discrete ground state of energy m (corresponding to toy gravitons forming the black hole), and a gapless continuous spectrum (to accommodate for the Hawking radiation with energy ω >m ). Each constituent is in a superposition of the ground state and a Planckian distribution at the expected Hawking temperature in the continuum. We first find that, assuming the Hawking radiation is the leading effect of the internal scatterings, the corresponding N -particle state can be collectively described by a single-particle wave function given by a superposition of a total ground state with energy M =N m and a Planckian distribution for E >M at the same Hawking temperature. From this collective state, we compute the partition function and obtain an entropy which reproduces the usual area law with a logarithmic correction precisely related with the Hawking component. By means of the horizon wave function for the system, we finally show the backreaction of modes with ω >m reduces the Hawking flux. Both corrections, to the entropy and to the Hawking flux, suggest the evaporation properly stops for vanishing mass, if the black hole is in this particular quantum state.
Myers, R C
2001-01-01
This is a short summary of my lectures given at the Fourth Mexican School on Gravitation and Mathematical Physics. These lectures gave a brief introduction to black holes in string theory, in which I primarily focussed on describing some of the recent calculations of black hole entropy using the statistical mechanics of D-brane states. The following overview will also provide the interested students with an introduction to the relevant literature.
Matsueda, Hiroaki; Hashizume, Yoichiro
2012-01-01
A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.
Comments on Black Holes in Matrix Theory
Horowitz, Gary T.; Martinec, Emil J.
1997-01-01
The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes black strings stretched across the longitudinal direction, near the transition where black strings become unstable to the formation of black holes. It is argued that the appropriate dynamics on the other (black hole) side of the transition is that of the zero m...
Energy Technology Data Exchange (ETDEWEB)
NONE
2002-02-01
instance, the UK's research councils have yet to put any real money behind these ideas. Black holes are best described by the general theory of relativity. However, general relativity is a classical theory of gravity, and although its predictions have been verified in many experiments, a quantum theory of gravity remains one of the holy grails of physics. One of the first physicists to make real progress in this quest to reconcile general relativity and quantum mechanics was Stephen Hawking. In 1974 Hawking calculated what would happen if a quantum fluctuation occurred near an event horizon. He concluded that the black hole would radiate, and that the amount of radiation would be inversely proportional to the mass of the black hole. However, black holes tend to be very heavy, so their output of Hawking radiation would be too low to detect experimentally. One intriguing exception could be much smaller primordial black holes created in the big bang: these should radiate observable amounts of gamma rays, but they have not been detected yet. This whole body of work - in which thermodynamic concepts such as temperature and entropy are also associated with the black hole - is Hawking's major achievement in physics. The detection of Hawking radiation is the ultimate goal of experiments on artificial black holes, although a lot of theoretical and experimental work has to be done first. The successful experiment is likely to involve a flowing Bose-Einstein condensate or a medium in which the speed of light can be reduced to zero. After years of groundwork, physicists have recently made rapid progress in both these fields. Meanwhile, the recent observation of neutrons in discrete quantum states in a gravitational potential shows that quantum gravity effects can be seen in the laboratory. All that is needed now is an act of faith. (U.K.)
Black Hole Final State Conspiracies
McInnes, Brett
2008-01-01
The principle that unitarity must be preserved in all processes, no matter how exotic, has led to deep insights into boundary conditions in cosmology and black hole theory. In the case of black hole evaporation, Horowitz and Maldacena were led to propose that unitarity preservation can be understood in terms of a restriction imposed on the wave function at the singularity. Gottesman and Preskill showed that this natural idea only works if one postulates the presence of "conspiracies" between systems just inside the event horizon and states at much later times, near the singularity. We argue that some AdS black holes have unusual internal thermodynamics, and that this may permit the required "conspiracies" if real black holes are described by some kind of sum over all AdS black holes having the same entropy.
Thermodynamics of Lifshitz black holes
Devecioǧlu, Deniz Olgu; Sarıoǧlu, Özgür
2011-06-01
We apply the recently extended conserved Killing charge definition of Abbott-Deser-Tekin formalism to compute, for the first time, the energies of analytic Lifshitz black holes in higher dimensions. We then calculate the temperature and the entropy of this large family of solutions, and study and discuss the first law of black hole thermodynamics. Along the way we also identify the possible critical points of the relevant quadratic curvature gravity theories. Separately, we also apply the generalized Killing charge definition to compute the energy and the angular momentum of the warped AdS3 black hole solution of the three-dimensional new massive gravity theory.
Critelli, Renato; Finazzo, Stefano I; Noronha, Jorge
2016-01-01
We investigate the temperature and magnetic field dependence of the Polyakov loop and heavy quark entropy in a bottom-up Einstein-Maxwell-dilaton (EMD) holographic model for the strongly coupled quark-gluon plasma (QGP) that quantitatively matches lattice data for the $(2+1)$-flavor QCD equation of state at finite magnetic field and physical quark masses. We compare the holographic EMD model results for the Polyakov loop at zero and nonzero magnetic fields and the heavy quark entropy at vanishing magnetic field with the latest lattice data available for these observables and find good agreement for temperatures $T\\gtrsim 150$ MeV and magnetic fields $eB\\lesssim 1$ GeV$^2$. Predictions for the behavior of the heavy quark entropy at nonzero magnetic fields are made that could be readily tested on the lattice.
Entropy of a charged black hole in two dimensions without cutoff
Kim, Wontae; Kim, Yong-Wan; Park, Young-Jai
2007-01-01
By introducing the generalized uncertainty principle (GUP) on quantum density states, we newly obtain a consistent entropy of a scalar field on the (1+1)-dimensional Maxwell-dilaton background without an artificial cutoff in contrast to the results of the brick wall model, which depend on the choice of the Hawking temperature for the extremal case.
From Schwinger Balls to Black Holes
Allahbakhshi, Davood
2016-01-01
We have shown intriguing similarities between Schwinger balls and black holes. By considering black hole as a gravitational Schwinger ball, we have derived the Bekenstein-Hawking entropy and the first law of black hole thermodynamics as a direct result of the inverse area dependence of the gravitational force. It is also shown that the Planck length is nothing but the gravitational Schwinger length. The relation between the mass and the radius of the black hole is derived by considering the black hole as a Schwinger ball of gravitons. We show how the evolution of the entanglement entropy of the black hole, as Page introduced many years ago, can be obtained by including gravitons in the black hole's evaporation process and using a deformed EPR mechanism. Also this deformed EPR mechanism can solve the information paradox. We show how naive simultaneous usage of Page's argument and equivalence principle leads to firewall problem.
Bastos, C.; Bertolami, O.; Dias, N. C.; Prata, J. N.
2010-04-01
One considers phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model to study the interior of a Schwarzschild black hole. It is shown that the potential function of the corresponding quantum cosmology problem has a local minimum. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity parameter, η. Furthermore, the t = r = 0 singularity is analysed in the noncommutative regime and it is shown that the wave function vanishes in this limit.
Energy Technology Data Exchange (ETDEWEB)
Bastos, C; Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisboa (Portugal); Dias, N C; Prata, J N, E-mail: cbastos@fisica.ist.utl.p, E-mail: orfeu@cosmos.ist.utl.p, E-mail: ncdias@mail.telepac.p, E-mail: joao.prata@mail.telepac.p [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande, 376, 1749-024 Lisboa (Portugal)
2010-04-01
One considers phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model to study the interior of a Schwarzschild black hole. It is shown that the potential function of the corresponding quantum cosmology problem has a local minimum. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity parameter, {eta}. Furthermore, the t = r = 0 singularity is analysed in the noncommutative regime and it is shown that the wave function vanishes in this limit.
International Nuclear Information System (INIS)
One considers phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model to study the interior of a Schwarzschild black hole. It is shown that the potential function of the corresponding quantum cosmology problem has a local minimum. One deduces the thermodynamics and show that the Hawking temperature and entropy exhibit an explicit dependence on the momentum noncommutativity parameter, η. Furthermore, the t = r = 0 singularity is analysed in the noncommutative regime and it is shown that the wave function vanishes in this limit.
Thermodynamics of black holes in rainbow gravity
Banerjee, Ritwick
2016-01-01
In this paper, we investigate the thermodynamic properties of black holes under the influence of rainbow gravity. In the metric of Schwarzschild, Reissner-Nordstrom and Reissner-Nordstrom-de-Sitter black hole surrounded by quintessence, we consider a rainbow function and derive the existence of remnant and critical masses of a black hole. Using the Hawking temperature relation we derive the heat capacity and the entropy of the rainbow gravity inspired black holes and closely study the relation between entropy and area of the horizon for different values of n of the rainbow function.
Black hole thermodynamics from Euclidean horizon constraints.
Carlip, S
2007-07-13
To explain black hole thermodynamics in quantum gravity, one must introduce constraints to ensure that a black hole is actually present. I show that for a large class of black holes, such "horizon constraints" allow the use of conformal field theory techniques to compute the density of states, reproducing the Bekenstein-Hawking entropy in a nearly model-independent manner. One standard string theory approach to black hole entropy arises as a special case, lending support to the claim that the mechanism may be "universal." I argue that the relevant degrees of freedom are Goldstone-boson-like excitations arising from the weak breaking of symmetry by the constraints. PMID:17678209
Implementing black hole as efficient power plant
Wei, Shao-Wen
2016-01-01
Treating the black hole molecules as working substance and considering its phase structure, we study the black hole heat engine by a charged anti-de Sitter black hole. In the reduced temperature-entropy chart, it is found that the work, heat, and efficiency of the engine are independent of the black hole charge. Applying the Rankine cycle with or without a back pressure mechanism to the black hole heat engine, the efficiency is numerically solved. The result shows that the black hole engine working along the Rankine cycle with a back pressure mechanism has a higher efficiency. This provides a novel and efficient mechanism to produce the useful mechanical work with black hole, and such heat engine may act as a possible energy source for the high energy astrophysical phenomena near the black hole.
Shmakova, Marina
1997-07-01
We find the entropy of N=2 extreme black holes associated with general Calabi-Yau moduli space and the prepotential F=dABC(XAXBXC/X0). We show that for arbitrary dABC and black hole charges p and q the entropy-area formula depends on combinations of these charges and parameters dABC. These combinations are the solutions of a simple system of algebraic equations. We give a few examples of particular Calabi-Yau moduli spaces for which this system has an explicit solution. For the special case when one of the black hole charges is equal to zero (p0=0) the solution always exists.
On the quantum aspects of the logarithmic corrections to the black hole entropy
Castro, C
2000-01-01
An extension of the conventional space-time to noncommutative Clifford manifolds where all p-branes are treated on equal footing allowed authors to write a master action functional. The respective functional equation is simplified and applied to the p-loop oscillator on Clifford manifolds. Its solution represents a generalization of the conventional quantum point oscillator which also extends to the region of the Planck scales. In the latter the solution yields in an elementary fashion the basic relations of string theory including string tension quantization. In addition, it is shown that the degeneracy of the $first$ collective excited state of the p-loop oscillator yields not only the well-known Bekenstein-Hawking area-entropy linear relation but also the logarithmic corrections therein.
Black hole information vs. locality
Itzhaki, N
1996-01-01
We discuss the limitations on space time measurement in Schwarzchild metric. We find that near the horizon the limitations on space time measurement are of the order of the black hole radius. We suggest that it indicates that a large mass black hole can not be described by means of local field theory even at macroscopic distances and that any attempt to describe black hole formation and evaporation by means of an effective local field theory will necessarily lead to information loss. We also present a new interpretation of the black hole entropy which leads to S=cA , where c is a constant of order 1 which does not depend on the number of fields.
Hayward, Sean A.
2008-01-01
This is a review of current theory of black-hole dynamics, concentrating on the framework in terms of trapping horizons. Summaries are given of the history, the classical theory of black holes, the defining ideas of dynamical black holes, the basic laws, conservation laws for energy and angular momentum, other physical quantities and the limit of local equilibrium. Some new material concerns how processes such as black-hole evaporation and coalescence might be described by a single trapping h...
Larjo, Klaus; Lowe, David A.; Thorlacius, Larus
2013-05-01
The postulates of black hole complementarity do not imply a firewall for infalling observers at a black hole horizon. The dynamics of the stretched horizon, that scrambles and reemits information, determines whether infalling observers experience anything out of the ordinary when entering a large black hole. In particular, there is no firewall if the stretched horizon degrees of freedom retain information for a time of the order of the black hole scrambling time.
Schwarzchild Black Holes in Matrix Theory, 2
Banks, T; Klebanov, Igor R; Susskind, Leonard
1998-01-01
We present a crude Matrix Theory model for Schwarzchild black holes in uncompactified dimension greater than 5. The model accounts for the size, entropy, and long range static interactions of black holes. The key feature of the model is a Boltzmann gas of D0 branes, a concept which depends on certain qualitative features of Matrix Theory which previously have not been utilized in studies of black holes.
Quantum Evaporation of Liouville Black Holes
Mann, R. B.
1993-01-01
The classical field equations of a Liouville field coupled to gravity in two spacetime dimensions are shown to have black hole solutions. Exact solutions are also obtained when quantum corrections due to back reaction effects are included, modifying both the ADM mass and the black hole entropy. The thermodynamic limit breaks down before evaporation of the black hole is complete, indicating that higher-loop effects must be included for a full description of the process. A scenario for the fina...
Better Late than Never: Information Retrieval from Black Holes
Braunstein, Sam; Pirandola, Stefano; Zyczkowski, Karol
2009-01-01
We show that, in order to preserve the equivalence principle until late times in unitarily evaporating black holes, the thermodynamic entropy of a black hole must be primarily entropy of entanglement across the event horizon. For such black holes, we show that the information entering a black hole becomes encoded in correlations within a tripartite quantum state, the quantum analogue of a one-time pad, and is only decoded into the outgoing radiation very late in the evaporation. This behavior...
Partition functions for supersymmetric black holes
J. Manschot
2008-01-01
This thesis presents a number of results on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view. Such a microscopic explanation was desired after the association of a
Directory of Open Access Journals (Sweden)
Roberto Casadio
2015-10-01
Full Text Available We review some features of Bose–Einstein condensate (BEC models of black holes obtained by means of the horizon wave function formalism. We consider the Klein–Gordon equation for a toy graviton field coupled to a static matter current in a spherically-symmetric setup. The classical field reproduces the Newtonian potential generated by the matter source, while the corresponding quantum state is given by a coherent superposition of scalar modes with a continuous occupation number. An attractive self-interaction is needed for bound states to form, the case in which one finds that (approximately one mode is allowed, and the system of N bosons can be self-confined in a volume of the size of the Schwarzschild radius. The horizon wave function formalism is then used to show that the radius of such a system corresponds to a proper horizon. The uncertainty in the size of the horizon is related to the typical energy of Hawking modes: it decreases with the increasing of the black hole mass (larger number of gravitons, resulting in agreement with the semiclassical calculations and which does not hold for a single very massive particle. The spectrum of these systems has two components: a discrete ground state of energy m (the bosons forming the black hole and a continuous spectrum with energy ω > m (representing the Hawking radiation and modeled with a Planckian distribution at the expected Hawking temperature. Assuming the main effect of the internal scatterings is the Hawking radiation, the N-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy M = Nm and Entropy 2015, 17 6894 a Planckian distribution for E > M at the same Hawking temperature. This can be used to compute the partition function and to find the usual area law for the entropy, with a logarithmic correction related to the Hawking component. The backreaction of modes with ω > m is also shown to reduce
Zhang, Tianxi
2014-06-01
The black hole universe model is a multiverse model of cosmology recently developed by the speaker. According to this new model, our universe is a fully grown extremely supermassive black hole, which originated from a hot star-like black hole with several solar masses, and gradually grew up from a supermassive black hole with million to billion solar masses to the present state with trillion-trillion solar masses by accreting ambient matter or merging with other black holes. The entire space is structured with infinite layers or universes hierarchically. The innermost three layers include the universe that we live, the inside star-like and supermassive black holes called child universes, and the outside space called mother universe. The outermost layer is infinite in mass, radius, and entropy without an edge and limits to zero for both the matter density and absolute temperature. All layers are governed by the same physics and tend to expand physically in one direction (outward or the direction of increasing entropy). The expansion of a black hole universe decreases its density and temperature but does not alter the laws of physics. The black hole universe evolves iteratively and endlessly without a beginning. When one universe expands out, a new similar one is formed from inside star-like and supermassive black holes. In each of iterations, elements are resynthesized, matter is reconfigurated, and the universe is renewed rather than a simple repeat. The black hole universe is consistent with the Mach principle, observations, and Einsteinian general relativity. It has only one postulate but is able to explain all phenomena occurred in the universe with well-developed physics. The black hole universe does not need dark energy for acceleration and an inflation epoch for flatness, and thus has a devastating impact on the big bang model. In this talk, I will present how this new cosmological model explains the various aspects of the universe, including the origin
Arbona, A; Carot, J; Mas, L; Massó, J; Stela, J
1998-01-01
Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric is the vacuum solution obtained by the well known conformal imaging method. The interior metric for every black hole is regular everywhere and corresponds to a positive energy density. The resulting matched solutions cover then the whole initial (Cauchy) hypersurface, without any singularity, and can be useful for numerical applications. The simpler cases of one black hole (Schwarzschild data) or two identical black holes (Misner data) are explicitly solved. A procedure for extending this construction to the multiple black hole case is also given, and it is shown to work for all time symmetric vacuum solutions obtained by the conformal imaging method. The numerical evolution of one such 'stuffed' black hole is compared with that of a pure vacuum or 'plain' black hole in the...
Neitzke, A; Vandoren, S; Neitzke, Andrew; Pioline, Boris; Vandoren, Stefan
2007-01-01
Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \\Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function ...
Thermal corpuscular black holes
Casadio, Roberto; Orlandi, Alessio
2015-01-01
We study the corpuscular model of an evaporating black hole consisting of a specific quantum state for a large number $N$ of self-confined bosons. The single-particle spectrum contains a discrete ground state of energy $m$ (corresponding to toy gravitons forming the black hole), and a gapless continuous spectrum (to accommodate for the Hawking radiation with energy $\\omega>m$). Each constituent is in a superposition of the ground state and a Planckian distribution at the expected Hawking temperature in the continuum. We first find that, assuming the Hawking radiation is the leading effect of the internal scatterings, the corresponding $N$-particle state can be collectively described by a single-particle wave-function given by a superposition of a total ground state with energy $M=N\\,m$ and a Planckian distribution for $E>M$ at the same Hawking temperature. From this collective state, we compute the partition function and obtain an entropy which reproduces the usual area law with a logarithmic correction preci...
Voros product and noncommutative inspired black holes
Gangopadhyay, Sunandan
2013-01-01
We emphasize the importance of the Voros product in defining noncommutative inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordstr\\"{o}m black holes show that the area law holds upto order $\\frac{1}{\\sqrt{\\theta}}e^{-M^2/\\theta}$. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy $E$ for these black holes is then obtained and a deviation from the standard identity $E=2ST_H$ is found at the order $\\sqrt{\\theta}e^{-M^2/\\theta}$. This deviation leads to a nonvanishing Komar energy at the extremal point $T_{H}=0$ of these black holes. The Smarr formula is finally worked out for the noncommutative Schwarzschild black hole. Similar features also exist for a deSitter--Schwarzschild geometry.
Voros Product and Noncommutative Inspired Black Holes
Gangopadhyay, Sunandan
2013-03-01
We emphasize the importance of the Voros product in defining the noncommutative (NC) inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner-Nordström (RN) black holes show that the area law holds up to order (1)/(√ {θ )}e-M2/θ . The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy E for these black holes is then obtained and a deviation from the standard identity E = 2STH is found at the order √ {θ }e-M2/θ . This deviation leads to a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. The Smarr formula is finally worked out for the NC Schwarzschild black hole. Similar features also exist for a de Sitter-Schwarzschild geometry.
Black Hole Thermodynamics Based on Unitary Evolutions
Feng, Yu-Lei
2015-01-01
In this paper, we try to construct black hole thermodynamics based on the fact that, the formation and evaporation of a black hole can be described by quantum unitary evolutions. First, we show that the Bekenstein-Hawking entropy $S_{BH}$ cannot be a Boltzmann or thermal entropy. To confirm this statement, we show that the original black hole's "first law" cannot be treated as the first law of thermodynamics formally, due to some missing metric perturbations caused by matter. Then, by including those (quantum) metric perturbations, we show that the black hole formation and evaporation can be described in a unitary manner effectively, through a quantum channel between the exterior and interior of the event horizon. In this way, the paradoxes of information loss and firewall can be resolved effectively. Finally, we show that black hole thermodynamics can be constructed in an ordinary way, by constructing statistical mechanics.
Black hole thermodynamics based on unitary evolutions
Feng, Yu-Lei; Chen, Yi-Xin
2015-10-01
In this paper, we try to construct black hole thermodynamics based on the fact that the formation and evaporation of a black hole can be described by quantum unitary evolutions. First, we show that the Bekenstein-Hawking entropy SBH may not be a Boltzmann or thermal entropy. To confirm this statement, we show that the original black hole's ‘first law’ may not simply be treated as the first law of thermodynamics formally, due to some missing metric perturbations caused by matter. Then, by including those (quantum) metric perturbations, we show that the black hole formation and evaporation can be described effectively in a unitary manner, through a quantum channel between the exterior and interior of the event horizon. In this way, the paradoxes of information loss and firewall can be resolved effectively. Finally, we show that black hole thermodynamics can be constructed in an ordinary way, by constructing statistical mechanics.
Scrambling with matrix black holes
Brady, Lucas; Sahakian, Vatche
2013-08-01
If black holes are not to be dreaded sinks of information but rather fully described by unitary evolution, they must scramble in-falling data and eventually leak it through Hawking radiation. Sekino and Susskind have conjectured that black holes are fast scramblers; they generate entanglement at a remarkably efficient rate, with the characteristic time scaling logarithmically with the entropy. In this work, we focus on Matrix theory—M-theory in the light-cone frame—and directly probe the conjecture. We develop a concrete test bed for quantum gravity using the fermionic variables of Matrix theory and show that the problem becomes that of chains of qubits with an intricate network of interactions. We demonstrate that the black hole system evolves much like a Brownian quantum circuit, with strong indications that it is indeed a fast scrambler. We also analyze the Berenstein-Maldacena-Nastase model and reach the same tentative conclusion.
Stimulated Black Hole Evaporation
Spaans, Marco
2016-01-01
Black holes are extreme expressions of gravity. Their existence is predicted by Einstein's theory of general relativity and is supported by observations. Black holes obey quantum mechanics and evaporate spontaneously. Here it is shown that a mass rate $R_f\\sim 3\\times 10^{-8} (M_0/M)^{1/2}$ $M_0$ yr$^{-1}$ onto the horizon of a black hole with mass $M$ (in units of solar mass $M_0$) stimulates a black hole into rapid evaporation. Specifically, $\\sim 3 M_0$ black holes can emit a large fraction of their mass, and explode, in $M/R_f \\sim 3\\times 10^7 (M/M_0)^{3/2}$ yr. These stimulated black holes radiate a spectral line power $P \\sim 2\\times 10^{39} (M_0/M)^{1/2}$ erg s$^{-1}$, at a wavelength $\\lambda \\sim 3\\times 10^5 (M/M_0)$ cm. This prediction can be observationally verified.
Gonzalez, P A; Saavedra, Joel; Vasquez, Yerko
2014-01-01
We consider a gravitating system consisting of a scalar field minimally coupled to gravity with a self-interacting potential and an U(1) electromagnetic field. Solving the coupled Einstein-Maxwell-scalar system we find exact hairy charged black hole solutions with the scalar field regular everywhere. We go to the zero temperature limit and we study the effect of the scalar field on the near horizon geometry of an extremal black hole. We find that except a critical value of the charge of the black hole there is also a critical value of the charge of the scalar field beyond of which the extremal black hole is destabilized. We study the thermodynamics of these solutions and we find that if the space is flat then at low temperature the Reissner-Nordstr\\"om black hole is thermodynamically preferred, while if the space is AdS the hairy charged black hole is thermodynamically preferred at low temperature.
Gorini, Vittorio; Moschella, Ugo; Treves, Aldo; Colpi, Monica
2016-01-01
Based on graduate school lectures in contemporary relativity and gravitational physics, this book gives a complete and unified picture of the present status of theoretical and observational properties of astrophysical black holes. The chapters are written by internationally recognized specialists. They cover general theoretical aspects of black hole astrophysics, the theory of accretion and ejection of gas and jets, stellar-sized black holes observed in the Milky Way, the formation and evolution of supermassive black holes in galactic centers and quasars as well as their influence on the dynamics in galactic nuclei. The final chapter addresses analytical relativity of black holes supporting theoretical understanding of the coalescence of black holes as well as being of great relevance in identifying gravitational wave signals. With its introductory chapters the book is aimed at advanced graduate and post-graduate students, but it will also be useful for specialists.
Perturbations around black holes
Wang, B
2005-01-01
Perturbations around black holes have been an intriguing topic in the last few decades. They are particularly important today, since they relate to the gravitational wave observations which may provide the unique fingerprint of black holes' existence. Besides the astrophysical interest, theoretically perturbations around black holes can be used as testing grounds to examine the proposed AdS/CFT and dS/CFT correspondence.
Begelman, Mitchell C
2003-06-20
Black holes are common objects in the universe. Each galaxy contains large numbers-perhaps millions-of stellar-mass black holes, each the remnant of a massive star. In addition, nearly every galaxy contains a supermassive black hole at its center, with a mass ranging from millions to billions of solar masses. This review discusses the demographics of black holes, the ways in which they interact with their environment, factors that may regulate their formation and growth, and progress toward determining whether these objects really warp spacetime as predicted by the general theory of relativity. PMID:12817138
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Arsiwalla, Xerxes D
2009-01-01
We study the problem of spatially stabilising four dimensional extremal black holes in background electric/magnetic fields. Whilst looking for stationary stable solutions describing black holes kept in external fields we find that taking a continuum limit of Denef et al's multi-center solutions provides a supergravity description of such backgrounds within which a black hole can be trapped in a given volume. This is realised by levitating a black hole over a magnetic dipole base. We comment on how such a construction resembles a mechanical Levitron.
Neves, J C S
2015-01-01
In this work, we have deformed regular black holes which possess a general mass term described by a function which generalizes the Bardeen and Hayward mass terms. Using linear constraints in the energy-momentum tensor, the solutions are either regular or singular. That is, with this approach, it is possible to generate singular black holes from regular black holes and vice versa. Moreover, contrary to the Bardeen and Hayward regular solutions, the regular deformed metrics may violate the weak energy condition despite the presence of the spherical symmetry. Some comments on accretion of deformed black holes in cosmological scenarios are made.
New Horizons for Black Holes and Branes
Emparan, Roberto; Niarchos, Vasilis; Obers, Niels A
2009-01-01
We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreove...
Introduction to General Relativity and Black Holes (3/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (5/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (2/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (1/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Introduction to General Relativity and Black Holes (4/5)
CERN. Geneva
2001-01-01
Conceptual foundations of General Relativity (GR). Uniqueness of GR. Mathematical framework: tensor calculus, Riemannian geometry, connection, 'spin' connection, curvature, Cartan's form calculus. Hilbert-Einstein action, Einstein equations. Weak gravitational fields. Post Newtonian Approximation. Gravitanional Waves. Exact solutions. Killing vectors. Experimental tests. Black Holes: extensions of the Schwarzschild solution; Kerr-Newman holes; no-hair theorems; energtics of black holes; the membrane approach; quantum mechanics of black holes; Bekenstein entropy; Hawking temperature; black holes and string theory.
Charge Fluctuations of an Uncharged Black Hole
Schiffer, Marcelo
2016-01-01
In this paper we calculate charge fluctuations of a Schwarzschild black-hole of mass $M$ confined within a perfectly reflecting cavity of radius R in thermal equilibrium with various species of radiation and fermions . Charge conservation is constrained by a Lagrange multiplier (the chemical potential). Black hole charge fluctuations are expected owing to continuous absorption and emission of particles by the black hole. For black holes much more massive than $10^{16} g$ , these fluctuations are exponentially suppressed. For black holes lighter than this, the Schwarzschild black hole is unstable under charge fluctuations for almost every possible size of the confining vessel. The stability regime and the fluctuations are calculated through the second derivative of the entropy with respect to the charge. The expression obtained contains many puzzling terms besides the expected thermodynamical fluctuations: terms corresponding to instabilities that do not depend on the specific value of charge of the charge car...
Black hole chemistry: thermodynamics with Lambda
Kubiznak, David; Teo, Mae
2016-01-01
We review recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. In this approach, the mass of the black hole is no longer regarded as internal energy, rather it is identified with the chemical enthalpy. This leads to an extended dictionary for black hole thermodynamic quantities, in particular a notion of thermodynamic volume emerges for a given black hole spacetime. This volume is conjectured to satisfy the reverse isoperimetric inequality - an inequality imposing a bound on the amount of entropy black hole can carry for a fixed thermodynamic volume. New thermodynamic phase transitions naturally emerge from these identifications. Namely, we show that black holes can be understood from the viewpoint of chemistry, in terms of concepts such as Van der Waals fluids, reentrant phase transitions, and triple points. We also review the recent attempts at exten...
Information Retention by Stringy Black Holes
AUTHOR|(CDS)2108556
2015-01-01
Building upon our previous work on two-dimensional stringy black holes and its extension to spherically-symmetric four-dimensional stringy black holes, we show how the latter retain information. A key r\\^ole is played by an infinite-dimensional $W_\\infty$ symmetry that preserves the area of an isolated black-hole horizon and hence its entropy. The exactly-marginal conformal world-sheet operator representing a massless stringy particle interacting with the black hole necessarily includes a contribution from $W_\\infty$ generators in its vertex function. This admixture manifests the transfer of information between the string black hole and external particles. We discuss different manifestations of $W_\\infty$ symmetry in black-hole physics and the connections between them.
Anti-de Sitter Spaces and Nonextreme Black Holes
Larsen, F
1998-01-01
At low energy the near horizon geometry of nonextreme black holes in four dimensions exhibits an effective SL(2,R)_L x SL(2,R)_R symmetry. The parameters of the corresponding induced conformal field theory gives the correct expression for the black hole entropy. The resulting spectrum of the Schwarzchild black hole is compared with another proposal.
Stationary Configurations and Geodesic Description of Supersymmetric Black Holes
Käppeli, Jürg
2003-01-01
This thesis contains a detailed study of various properties of supersymmetric black holes. In chapter I an overview over some of the fascinating aspects of black hole physics is provided. In particular, the string theory approach to black hole entropy is discussed. One of the consequences of the str
DEFF Research Database (Denmark)
Kragh, Helge Stjernholm
2016-01-01
Review essay, Marcia Bartusiak, Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled On by Hawking Became Loved (New Haven: Yale University Press, 2015).......Review essay, Marcia Bartusiak, Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, and Gambled On by Hawking Became Loved (New Haven: Yale University Press, 2015)....
Andersson, N
2000-01-01
This is a chapter on Black-hole Scattering that was commissioned for an Encyclopaedia on Scattering edited by Pike and Sabatier, to be published by Academic Press. The chapter surveys wave propagation in black-hole spacetimes, diffraction effects in wave scattering, resonances, quasinormal modes and related topics.
Noncommutative Singular Black Holes
International Nuclear Information System (INIS)
In this paper, applying the method of coordinate coherent states to describe a noncommutative model of Vaidya black holes leads to an exact (t - r) dependence of solution in terms of the noncommutative parameter σ. In this setup, there is no black hole remnant at long times.
Noncommutative Singular Black Holes
Hamid Mehdipour, S.
2010-11-01
In this paper, applying the method of coordinate coherent states to describe a noncommutative model of Vaidya black holes leads to an exact (t — r) dependence of solution in terms of the noncommutative parameter σ. In this setup, there is no black hole remnant at long times.
Indian Academy of Sciences (India)
Koustubh Ajit Kabe
2012-09-01
In the following paper, certain black hole dynamic potentials have been developed definitively on the lines of classical thermodynamics. These potentials have been refined in view of the small differences in the equations of the laws of black hole dynamics as given by Bekenstein and those of thermodynamics. Nine fundamental black hole dynamical relations have been developed akin to the four fundamental thermodynamic relations of Maxwell. The specific heats , and , have been defined. For a black hole, these quantities are negative. The d equation has been obtained as an application of these fundamental relations. Time reversible processes observing constancy of surface gravity are considered and an equation connecting the internal energy of the black hole , the additional available energy defined as the first free energy function , and the surface gravity , has been obtained. Finally as a further application of the fundamental relations, it has been proved for a homogeneous gravitational field in black hole space times or a de Sitter black hole that $C_{\\Omega,\\Phi}-C_{J,Q}=\\kappa \\left[\\left(\\dfrac{\\partial J}{\\partial \\kappa}\\right)_{\\Omega,\\Phi}\\left(\\dfrac{\\partial \\Omega}{\\partial \\kappa}\\right)_{J,Q}+\\left(\\dfrac{\\partial Q}{\\partial \\kappa}\\right)_{\\Omega,\\Phi}\\left(\\dfrac{\\partial\\Phi}{\\partial \\kappa}\\right)_{J,Q}\\right]$. This is dubbed as the homogeneous fluid approximation in context of the black holes.
Better late than never: information retrieval from black holes.
Braunstein, Samuel L; Pirandola, Stefano; Życzkowski, Karol
2013-03-01
We show that, in order to preserve the equivalence principle until late times in unitarily evaporating black holes, the thermodynamic entropy of a black hole must be primarily entropy of entanglement across the event horizon. For such black holes, we show that the information entering a black hole becomes encoded in correlations within a tripartite quantum state, the quantum analogue of a one-time pad, and is only decoded into the outgoing radiation very late in the evaporation. This behavior generically describes the unitary evaporation of highly entangled black holes and requires no specially designed evolution. Our work suggests the existence of a matter-field sum rule for any fundamental theory.
Lifshitz Topological Black Holes
Mann, R B
2009-01-01
I find a class of black hole solutions to a (3+1) dimensional theory gravity coupled to abelian gauge fields with negative cosmological constant that has been proposed as the dual theory to a Lifshitz theory describing critical phenomena in (2+1) dimensions. These black holes are all asymptotic to a Lifshitz fixed point geometry and depend on a single parameter that determines both their area (or size) and their charge. Most of the solutions are obtained numerically, but an exact solution is also obtained for a particular value of this parameter. The thermodynamic behaviour of large black holes is almost the same regardless of genus, but differs considerably for small black holes. Screening behaviour is exhibited in the dual theory for any genus, but the critical length at which it sets in is genus-dependent for small black holes.
Evolution of massive black holes
Volonteri, Marta
2007-01-01
Supermassive black holes are nowadays believed to reside in most local galaxies. Accretion of gas and black hole mergers play a fundamental role in determining the two parameters defining a black hole: mass and spin. I briefly review here some of the physical processes that are conducive to the evolution of the massive black hole population. I'll discuss black hole formation processes that are likely to place at early cosmic epochs, and how massive black hole evolve in a hierarchical Universe...
Some Unique Constants Associated with Extremal Black Holes
Sivaram, C; 10.1007/s10509-012-0983-z
2012-01-01
In recent papers we had developed a unified picture of black hole entropy and curvature which was shown to lead to Hawking radiation. It was shown that for any black hole mass, holography implies a phase space of just one quantum associated with the interior of the black hole. Here we study extremal rotating and charged black holes and obtain unique values for ratios of angular momentum to entropy, charge to entropy, etc. It turns out that these ratios can be expressed in terms of fundamental constants in nature, having analogies with other physical systems, like in condensed matter physics.
Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole
International Nuclear Information System (INIS)
Few years ago, Setare (2006) has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula
Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole
Directory of Open Access Journals (Sweden)
G. Abbas
2014-01-01
Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.
Ahn, Eun-Joo; Cavaglia, Marco
2003-01-01
Production of high-energy gravitational objects is a common feature of gravitational theories. The primordial universe is a natural setting for the creation of black holes and other nonperturbative gravitational entities. Cosmic black holes can be used to probe physical properties of the very early universe which would usually require the knowledge of the theory of quantum gravity. They may be the only tool to explore thermalisation of the early universe. Whereas the creation of cosmic black ...
Black Hole Critical Phenomena Without Black Holes
Liebling, S L
2000-01-01
Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.
Note on black hole radiation spectrum in Loop Quantum Gravity
Diaz-Polo, Jacobo
2007-01-01
Recent detailed analysis within the Loop Quantum Gravity calculation of black hole entropy show a stair-like structure in the behavior of entropy as a function of horizon area. The non-trivial distribution of the degeneracy of the black hole horizon area eigenstates is at the origin of this behavior. This degeneracy distribution is analyzed and a phenomenological model is put forward to study the possible implications of this distribution in the black hole radiation spectrum.
Thermodynamical quantities around a RNAdS black hole
Institute of Scientific and Technical Information of China (English)
Mi Li-Qin; Li Zhong-Heng
2006-01-01
The entropy density, energy density, pressure and equation of state around the RNAdS black hole are calculated in the WKB approximation on the Teukolsky-type master equation. The appearance of spin-dependent terms is demonstrated. The existence of these terms shows that the black hole radiation is not exactly thermal radiation and the black hole entropy is not strictly proportional to the area of the event horizon.
Black hole spectroscopy from Loop Quantum Gravity models
Barrau, A.; Cao, Xiangyu; Noui, Karim; Perez, Alejandro
2015-01-01
Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter $\\gamma$. Starting with black holes of initial horizon area $A \\sim 10^2$ in Planck units, we present the...
Black hole thermodynamics and information loss in two dimensions
Fiola, T M; Strominger, A; Trivedi, S P; Thomas M Fiola; John Preskill; Andrew Strominger; Sandip P Trivedi
1994-01-01
Black hole evaporation is investigated in a (1+1)-dimensional model of quantum gravity. Quantum corrections to the black hole entropy are computed, and the fine-grained entropy of the Hawking radiation is studied. A generalized second law of thermodynamics is formulated, and shown to be valid under suitable conditions. It is also shown that, in this model, a black hole can consume an arbitrarily large amount of information.
CFT duals for accelerating black holes
Astorino, Marco
2016-09-01
The near horizon geometry of the rotating C-metric, describing accelerating Kerr-Newman black holes, is analysed. It is shown that, at extremality, even though it is not isomorphic to the extremal Kerr-Newman, it remains a warped and twisted product of AdS2 ×S2. Therefore the methods of the Kerr/CFT correspondence can successfully be applied to build a CFT dual model, whose entropy reproduces, through the Cardy formula, the Bekenstein-Hawking entropy of the accelerating black hole. The mass of accelerating Kerr-Newman black hole, which fulfils the first law of thermodynamics, is presented. Further generalisation in presence of an external Melvin-like magnetic field, used to regularise the conical singularity characteristic of the C-metrics, shows that the Kerr/CFT correspondence can be applied also for the accelerating and magnetised extremal black holes.
CFT Duals for Accelerating Black Holes
Astorino, Marco
2016-01-01
The near horizon geometry of the rotating C-metric, describing accelerating Kerr-Newman black holes, is analysed. It is shown that, at extremality, even though not it is isomorphic to the extremal Kerr-Newman, it remains a warped and twisted product of $AdS_2 \\times S^2$. Therefore the methods of the Kerr/CFT correspondence can successfully be applied to build a CFT dual model, whose entropy reproduce, through the Cardy formula, the Beckenstein-Hawking entropy of the accelerating black hole. The mass of accelerating Kerr-Newman black hole, which fulfil the first law of thermodynamics, is presented. Further generalisation in presence of an external Melvin-like magnetic field, used to regularise the conical singularity characteristic of the C-metrics, shows that the Kerr/CFT correspondence can be applied also for the accelerating and magnetised extremal black holes.
Geometric Product Formula for Charged Accelerating Black Hole
Pradhan, Parthapratim
2016-01-01
We evaluate the geometric product formula i.e. area (or entropy) product formula of outer horizon (${\\cal H}^{+}$) and inner horizon (${\\cal H}^{-}$) for charged accelerating black hole. We find that mass-independent area functional relation of ${\\cal H}^{\\pm}$ for this black hole in terms of black hole charge, acceleration, cosmological constant and \\emph{cosmic string tension} respectively. We also compute the \\emph{Penrose inequality} for this black hole. Finally we compute the specific heat for this BH to determine the local thermodynamic stability of this black hole. Under certain criterion the black hole displayed second order phase transition.
Kleihaus, Burkhard; Yazadjiev, Stoytcho
2015-01-01
In the presence of a complex scalar field scalar-tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and ordinary hairy black holes. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.
Noncommutative Solitonic Black Hole
Chang-Young, Ee; Lee, Daeho; Lee, Youngone
2012-01-01
We investigate solitonic black hole solutions in three dimensional noncommutative spacetime. We do this in gravity with negative cosmological constant coupled to a scalar field using the Moyal product expanded up to first order in the noncommutativity parameter in the two noncommutative spatial directions. By numerical simulation we look for black hole solutions by increasing the non- commutativity parameter value starting from regular solutions with vanishing noncommutativity. We find that even a regular soliton solution in the commutative case becomes a black hole solution when the noncommutativity parameter reaches a certain value.
Energy Technology Data Exchange (ETDEWEB)
Kleihaus, Burkhard, E-mail: b.kleihaus@uni-oldenburg.de [Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Kunz, Jutta [Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Yazadjiev, Stoytcho [Department of Theoretical Physics, Faculty of Physics, Sofia University, Sofia 1164 (Bulgaria)
2015-05-11
In the presence of a complex scalar field scalar–tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and hairy black holes of General Relativity. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.
Directory of Open Access Journals (Sweden)
Burkhard Kleihaus
2015-05-01
Full Text Available In the presence of a complex scalar field scalar–tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and hairy black holes of General Relativity. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.
Hayward, Sean Alan
2013-01-01
Black holes, once just fascinating theoretical predictions of how gravity warps space-time according to Einstein's theory, are now generally accepted as astrophysical realities, formed by post-supernova collapse, or as supermassive black holes mysteriously found at the cores of most galaxies, powering active galactic nuclei, the most powerful objects in the universe. Theoretical understanding has progressed in recent decades with a wider realization that local concepts should characterize black holes, rather than the global concepts found in textbooks. In particular, notions such as trapping h
International Nuclear Information System (INIS)
In the presence of a complex scalar field scalar–tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and hairy black holes of General Relativity. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn
Desperately Seeking Intermediate-Mass Black Holes
Frampton, Paul H.
2009-01-01
Observational searches for Intermediate Mass Black Holes (IMBHs), defined to have masses between 30 and 300,000 solar masses, provide limits which allow up to ten percent of what is presently identified as halo dark matter to be in the form of IMBHs. These concentrate entropy so efficiently that the halo contribution can be bigger than the core supermassive black hole. Formation of IMBHs is briefly discussed.
On the thermodynamics of Lifshitz black holes
Devecioglu, Deniz Olgu
2011-01-01
We apply the recently extended conserved Killing charge definition of Abbott-Deser-Tekin formalism to compute, for the first time, the energies of analytic Lifshitz black holes in higher dimensions. We then calculate the temperature and the entropy of this large family of solutions and find that imposing the first law of black hole thermodynamics puts, sometimes severe, extra constraints on the allowed values of the dynamical exponent, which is a characteristic of these spacetimes. Separately, we also apply the generalized Killing charge definition to compute the energy and the angular momentum of the warped AdS_3 black hole solution of the three-dimensional New Massive Gravity theory.
BTZ black holes inspired by noncommutative geometry
Rahaman, Farook; Kuhfittig, P. K. F.; Bhui, B. C.; Rahaman, Mosiur; Ray, Saibal; Mondal, U. F.
2013-04-01
In this paper, a Bañados-Teitelboim-Zanelli (BTZ) black hole [Phys. Rev. Lett. 69, 1849 (1992)] is constructed from an exact solution of the Einstein field equations in a (2+1)—dimensional anti—de Sitter spacetime in the context of noncommutative geometry. The BTZ black hole turns out to have either two horizons, no horizon, or a single horizon corresponding to a minimal mass. Certain thermodynamical properties are investigated, including Hawking temperature, entropy, and heat capacity. Also discussed is the geodesic structure of BTZ black holes for both massless and massive particles. In particular, it is shown that bound orbits for test particles are possible.
BTZ black holes inspired by noncommutative geometry
Rahaman, Farook; Bhui, B C; Rahaman, Masiur; Ray, Saibal; Mondal, U F
2013-01-01
In this paper a Banados, Teitelboim and Zanelli (BTZ) black hole is constructed from an exact solution of the Einstein field equations in a (2+1)-dimensional anti-de Sitter spacetime in the context of noncommutative geometry. The BTZ black hole turns out to have two horizons, no horizon or a single horizon corresponding to a minimal mass. Certain thermodynamical properties are investigated, including Hawking temperature, entropy and heat capacity. Also discussed is the geodesic structure of BTZ black holes for both massless and massive particles. In particular, it is shown that bound orbits for test particles are possible.
Ruffini, Remo; Wheeler, John A.
1971-01-01
discusses the cosmology theory of a black hole, a region where an object loses its identity, but mass, charge, and momentum are conserved. Include are three possible formation processes, theorized properties, and three way they might eventually be detected. (DS)
Topics in black hole evaporation
International Nuclear Information System (INIS)
Two major aspects of particle creation by gravitational fields of black holes are studied: the neutrino emission from rotating black holes; and interactions between scalar particles emitted by a black hole. Neutrino emission is investigated under three topics: The asymmetry of the angular dependence of neutrino emission from rotating black holes; the production of a local matter excess by rotating black holes in a baryon symmetric universe; and cosmological magnetic field generation by neutrinos from evaporating black holes. Finally the author studies the effects of interactions on the black hole evaporation process
Stornaiolo, Cosimo
2001-01-01
In this paper we propose a model for the formation of the cosmological voids. We show that cosmological voids can form directly after the collapse of extremely large wavelength perturbations into low-density black holes or cosmological black holes (CBH). Consequently the voids are formed by the comoving expansion of the matter that surrounds the collapsed perturbation. It follows that the universe evolves, in first approximation, according to the Einstein-Straus cosmological model. We discuss...
International Nuclear Information System (INIS)
No particle theory can be complete without gravity. Einstein's theory of gravity is of the Euler-Lagrange form, but standard quantization procedure fails. In quantum gravity the higher order interactions have a dimensionality different form the fundamental ones, because Newton's constant G has dimensions and the renormalization procedure fails. Another problem with quantum gravity is even more mysterious. Suppose that we had regularized the gravitational forces at the small distance end in the way that the weak intermediate vector boson regularized the fundamental 4-fermion interaction vertex of the weak interactions. Then what we discover is that the gravitational forces are unstable. Given sufficiently large amount of matter, it can collapse under its own weight. Classical general relativity tells us what will happen: a black hole is formed. But how is this formulated in quantum theory. S. Hawking observed that when a field theory is quantized in the background metric of a black hole, the black hole actually emits particles in a completely random thermal way. Apparently black holes are just another form of matter unstable against Hawking decay. Unfortunately this picture cannot be complete. The problem is that the quantum version of black holes has infinite phase space, and other symptoms of a run-away solution. Black holes are the heaviest and most compact forms of matter that can be imagined. A complete particle theory can have nothing but a spectrum of black-hole like objects at it high-energy end. This is why it is believed that a resolution of the black hole problem will in time disclose the complete small-distance structure of our world. 6 references
Govindarajan, T R
2016-01-01
Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states match nicely with what we would expect for black holes. Also they serve to model membrane mechanism for the black hole horizons in simpler contexts. The singular potentials can also mimic expanding boundaries elegantly, there by obtaining appropriately tuned radiation rates.
Black hole critical phenomena without black holes
Indian Academy of Sciences (India)
Steven L Liebling
2000-10-01
Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I brieﬂy review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.
Holographic effective actions from black holes
International Nuclear Information System (INIS)
Using the Wald's relation between the Noether charge of diffeomorphisms and the entropy for a generic spacetime possessing a bifurcation surface, we introduce a method to obtain a family of higher order derivatives effective actions from the entropy of black holes. We consider the entropy as the starting point and we analyze the procedure of derivation of the action functional. We specialize to a particular class of theories which simplifies the calculations, f(R) theories. We apply the procedure to loop quantum gravity and to a general class of log-corrected entropy formulas.
Babichev, Eugeny; Charmousis, Christos; Hassaine, Mokhtar
2015-05-01
We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero the gauge field reduces to a standard Maxwell field. By taking into account the symmetries of the action, we construct charged black hole solutions. Allowing the scalar field to softly break symmetries of spacetime we construct black holes where the scalar field is regular on the black hole event horizon. Some of these solutions can be interpreted as the equivalent of Reissner-Nordstrom black holes of scalar tensor theories with a non trivial scalar field. A self tuning black hole solution found previously is extended to the presence of dyonic charge without affecting whatsoever the self tuning of a large positive cosmological constant. Finally, for a general shift invariant scalar tensor theory we demonstrate that the scalar field Ansatz and method we employ are mathematically compatible with the field equations. This opens up the possibility for novel searches of hairy black holes in a far more general setting of Horndeski theory.
Ultramassive Black Hole Coalescence
Khan, Fazeel; Berczik, Peter
2015-01-01
Although supermassive black holes (SMBHs) correlate well with their host galaxies, there is an emerging view that outliers exist. Henize 2-10, NGC 4889, and NGC1277 are examples of SMBHs at least an order of magnitude more massive than their host galaxy suggests. The dynamical effects of such ultramassive central black holes is unclear. Here, we perform direct N-body simulations of mergers of galactic nuclei where one black hole is ultramassive to study the evolution of the remnant and the black hole dynamics in this extreme regime. We find that the merger remnant is axisymmetric near the center, while near the large SMBH influence radius, the galaxy is triaxial. The SMBH separation shrinks rapidly due to dynamical friction, and quickly forms a binary black hole; if we scale our model to the most massive estimate for the NGC1277 black hole, for example, the timescale for the SMBH separation to shrink from nearly a kiloparsec to less than a parsec is roughly 10 Myr. By the time the SMBHs form a hard binary, gr...
Science Teacher, 2005
2005-01-01
Scientists using NASA's Swift satellite say they have found newborn black holes, just seconds old, in a confused state of existence. The holes are consuming material falling into them while somehow propelling other material away at great speeds. "First comes a blast of gamma rays followed by intense pulses of x-rays. The energies involved are much…
Black holes and thermodynamics -- The first half century
Grumiller, Daniel; Salzer, Jakob
2014-01-01
Black hole thermodynamics emerged from the classical general relativistic laws of black hole mechanics, summarized by Bardeen-Carter-Hawking, together with the physical insights by Bekenstein about black hole entropy and the semi-classical derivation by Hawking of black hole evaporation. The black hole entropy law inspired the formulation of the holographic principle by 't Hooft and Susskind, which is famously realized in the gauge/gravity correspondence by Maldacena, Gubser-Klebanov-Polaykov and Witten within string theory. Moreover, the microscopic derivation of black hole entropy, pioneered by Strominger-Vafa within string theory, often serves as a consistency check for putative theories of quantum gravity. In this book chapter we review these developments over five decades, starting in the 1960ies.
Cosmic censorship inside black holes
Thorlacius, L
2006-01-01
A simple argument is given that a traversable Cauchy horizon inside a black hole is incompatible with unitary black hole evolution. The argument assumes the validity of black hole complementarity and applies to a generic black hole carrying angular momentum and/or charge. In the second part of the paper we review recent work on the semiclassical geometry of two-dimensional charged black holes.
Constraints on the Generalized Uncertainty Principle from Black Hole Thermodynamics
Gangopadhyay, Sunandan; Faizal, Mir
2015-01-01
In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading order corrections to the entropy of a black hole.
Thermodynamic Relations for Kiselev and Dilaton Black Hole
International Nuclear Information System (INIS)
We investigate the thermodynamics and phase transition for Kiselev black hole and dilaton black hole. Specifically we consider Reissner-Nordström black hole surrounded by radiation and dust and Schwarzschild black hole surrounded by quintessence, as special cases of Kiselev solution. We have calculated the products relating the surface gravities, surface temperatures, Komar energies, areas, entropies, horizon radii, and the irreducible masses at the Cauchy and the event horizons. It is observed that the product of surface gravities, product of surface temperature, and product of Komar energies at the horizons are not universal quantities for the Kiselev solutions while products of areas and entropies at both the horizons are independent of mass of the above-mentioned black holes (except for Schwarzschild black hole surrounded by quintessence). For charged dilaton black hole, all the products vanish. The first law of thermodynamics is also verified for Kiselev solutions. Heat capacities are calculated and phase transitions are observed, under certain conditions
On the evaporation and on other properties of black holes
International Nuclear Information System (INIS)
After a short discussion of the basic properties of black-hole physics, including the 'no-hair' theorems, the hypothesis of the 'cosmic censor' and the first and second law of black-hole dynamics, we proceed to the thermodynamics of black holes. The concepts of entropy and temperature of a black hole are explained and the generalized second law of black-hole dynamics is presented. We then discuss particle creation in the gravitational fields of black holes and their lifetime due to evaporation. After a digression on chaotic cosmology the possible formation of black holes in the carly universe is treated. Finally we discuss the last violent stages of the evaporation process of black holes and possible observational tests. A few remarks on white holes - though a totally different phenomenon - are included at the end for the sake of clarity. (orig.) 891 HK/orig. 892 MB
Black Holes with Multiple Charges and the Correspondence Principle
Yang, H
1998-01-01
We consider the entropy of near extremal black holes with multiple charges in the context of the recently proposed correspondence principle of Horowitz and Polchinski, including black holes with two, three and four Ramond-Ramond charges. We find that at the matching point the black hole entropy can be accounted for by massless open strings ending on the D-branes for all cases except a black hole with four Ramond-Ramond charges, in which case a possible resolution in terms of brane-antibrane excitations is considered.
Extremal Black Holes and First Law of Thermodynamics
Johnstone, Maria; Simon, Joan; Yavartanoo, Hossein
2013-01-01
We study the low temperature expansion of the first law of thermodynamics for near-extremal black holes. We show that for extremal black holes with non-vanishing entropy, the leading order contribution yields an expression for their extremal entropy in agreement with the entropy function result and the Cardy formula for the entropy of a two dimensional chiral conformal field theory (CFT). When their entropy vanishes due to the vanishing of a one-cycle on the horizon, such leading contribution is always compatible with the first law satisfied by a BTZ black hole. These results are universal and consistent both with the presence of local AdS2 and AdS3 near horizon throats for extremal black holes and with the suggested quantum microscopic descriptions (AdS2/CFT1, Kerr/CFT and EVH/CFT).
International Nuclear Information System (INIS)
Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH quasi-normal modes (QNMs) and interpreted them naturally in terms of quantum levels. In this work we improve such an analysis removing some approximations that have been implicitly used in our previous works and obtaining the corrected expressions for the formulas of the horizon's area quantization and the number of quanta of area and hence also for Bekenstein-Hawking entropy, its subleading corrections and the number of micro-states, i.e. quantities which are fundamental to realize the underlying quantum gravity theory, like functions of the QNMs quantum ''overtone'' number n and, in turn, of the BH quantum excited level. An approximation concerning the maximum value of n is also corrected. On the other hand, our previous results were strictly corrected only for scalar and gravitational perturbations. Here we show that the discussion holds also for vector perturbations. The analysis is totally consistent with the general conviction that BHs result in highly excited states representing both the ''hydrogen atom'' and the ''quasi-thermal emission'' in quantum gravity. Our BH model is somewhat similar to the semi-classical Bohr's model of the structure of a hydrogen atom. The thermal approximation of previous results in the literature is consistent with the results in this paper. In principle, such results could also have important implications for the BH information paradox. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Corda, Christian [Institute for Theoretical Physics and Advanced Mathematics (IFM) Einstein-Galilei, Prato (Italy); Istituto Universitario di Ricerca ' ' Santa Rita' ' , Prato (Italy); International Institute for Applicable Mathematics and Information Sciences (IIAMIS), Hyderabad (India)
2013-12-15
Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH quasi-normal modes (QNMs) and interpreted them naturally in terms of quantum levels. In this work we improve such an analysis removing some approximations that have been implicitly used in our previous works and obtaining the corrected expressions for the formulas of the horizon's area quantization and the number of quanta of area and hence also for Bekenstein-Hawking entropy, its subleading corrections and the number of micro-states, i.e. quantities which are fundamental to realize the underlying quantum gravity theory, like functions of the QNMs quantum ''overtone'' number n and, in turn, of the BH quantum excited level. An approximation concerning the maximum value of n is also corrected. On the other hand, our previous results were strictly corrected only for scalar and gravitational perturbations. Here we show that the discussion holds also for vector perturbations. The analysis is totally consistent with the general conviction that BHs result in highly excited states representing both the ''hydrogen atom'' and the ''quasi-thermal emission'' in quantum gravity. Our BH model is somewhat similar to the semi-classical Bohr's model of the structure of a hydrogen atom. The thermal approximation of previous results in the literature is consistent with the results in this paper. In principle, such results could also have important implications for the BH information paradox. (orig.)
Babichev, Eugeny; Hassaine, Mokhtar
2015-01-01
We consider an Abelian gauge field coupled to a particular truncation of Horndeski theory. The Galileon field has translation symmetry and couples non minimally both to the metric and the gauge field. When the gauge-scalar coupling is zero the gauge field reduces to a standard Maxwell field. By taking into account the symmetries of the action, we construct charged black hole solutions. Allowing the scalar field to softly break symmetries of spacetime we construct black holes where the scalar field is regular on the black hole event horizon. Some of these solutions can be interpreted as the equivalent of Reissner-Nordstrom black holes of scalar tensor theories with a non trivial scalar field. A self tuning black hole solution found previously is extended to the presence of dyonic charge without affecting whatsoever the self tuning of a large positive cosmological constant. Finally, for a general shift invariant scalar tensor theory we demonstrate that the scalar field Ansatz and method we employ are mathematic...
The Thermodynamic Limit for Black Holes in Loop Quantum Gravity
Barbero, Fernando; Villaseñor, Eduardo J. S.
2015-01-01
This contribution discusses the thermodynamic limit for black holes in loop quantum gravity by using the number-theoretic methods introduced to compute their entropy in this framework. We show how that the subdominant corrections for the entropy in this limit differ from the ones corresponding to the statistical entropy.
Black holes in full quantum gravity
International Nuclear Information System (INIS)
Quantum black holes have been studied extensively in quantum gravity and string theory, using various semiclassical or background-dependent approaches. We explore the possibility of studying black holes in the full non-perturbative quantum theory, without recurring to semiclassical considerations, and in the context of loop quantum gravity. We propose a definition of a quantum black hole as the collection of the quantum degrees of freedom that do not influence observables at infinity. From this definition, it follows that for an observer at infinity a black hole is described by an SU(2) intertwining operator. The dimension of the Hilbert space of such intertwiners grows exponentially with the horizon area. These considerations shed some light on the physical nature of the microstates contributing to the black hole entropy. In particular, it can be seen that the microstates being counted for the entropy have the interpretation of describing different horizon shapes. The space of black hole microstates described here is related to the one arrived at recently by Engle et al (2009, arXiv:0905.3168) and sometime ago by Smolin (1995, J. Math. Phys. 36 6417), but obtained here directly within the full quantum theory.
Quantum Tunneling in Black Holes
Majhi, Bibhas Ranjan
2011-01-01
This thesis is focussed towards the applications of the quantum tunneling mechanism to study black holes. Here we give a general frame work of the existing tunneling mechanism, both the radial null geodesic and Hamilton Jacobi methods. On the radial null geodesic method side, we study the modifications to the tunneling rate, Hawking temperature and the Bekenstein- Hawking area law by including the back reaction as well as non-commutative effects in the space-time. A reformulation of the Hamilton-Jacobi (HJ) method is first introduced. Based on this, a close connection between the quantum tunneling and the gravitational anomaly mechanisms to discuss Hawking effect, is put forwarded. An interesting advantage of this reformulated HJ method is that one can get directly the emission spectrum from the event horizon of the black hole, which was missing in the earlier literature. Also, the quantization of the entropy and area of a black hole is discussed in this method. Another part of the thesis is the introduction ...
Yang, Huan; Zimmerman, Aaron; Lehner, Luis
2015-02-27
We demonstrate that rapidly spinning black holes can display a new type of nonlinear parametric instability-which is triggered above a certain perturbation amplitude threshold-akin to the onset of turbulence, with possibly observable consequences. This instability transfers from higher temporal and azimuthal spatial frequencies to lower frequencies-a phenomenon reminiscent of the inverse cascade displayed by (2+1)-dimensional fluids. Our finding provides evidence for the onset of transitory turbulence in astrophysical black holes and predicts observable signatures in black hole binaries with high spins. Furthermore, it gives a gravitational description of this behavior which, through the fluid-gravity duality, can potentially shed new light on the remarkable phenomena of turbulence in fluids.
Yang, Huan; Zimmerman, Aaron; Lehner, Luis
2015-02-27
We demonstrate that rapidly spinning black holes can display a new type of nonlinear parametric instability-which is triggered above a certain perturbation amplitude threshold-akin to the onset of turbulence, with possibly observable consequences. This instability transfers from higher temporal and azimuthal spatial frequencies to lower frequencies-a phenomenon reminiscent of the inverse cascade displayed by (2+1)-dimensional fluids. Our finding provides evidence for the onset of transitory turbulence in astrophysical black holes and predicts observable signatures in black hole binaries with high spins. Furthermore, it gives a gravitational description of this behavior which, through the fluid-gravity duality, can potentially shed new light on the remarkable phenomena of turbulence in fluids. PMID:25768746
Thermodynamic phase transition in the rainbow Schwarzschild black hole
Energy Technology Data Exchange (ETDEWEB)
Gim, Yongwan; Kim, Wontae, E-mail: yongwan89@sogang.ac.kr, E-mail: wtkim@sogang.ac.kr [Department of Physics, Sogang University, Seoul 121-742 (Korea, Republic of)
2014-10-01
We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locally stable tiny black hole; however, the off-shell free energy tells us that this black hole should eventually tunnel into the stable large black hole. Finally, we discuss the reason why the temperature near the horizon is finite in the rainbow black hole by employing the running gravitational coupling constant, whereas it is divergent near the horizon in the ordinary Schwarzschild black hole.
Instability of black holes with a Gauss-Bonnet term
Energy Technology Data Exchange (ETDEWEB)
Ahn, Wha-Keun; Gwak, Bogeun; Lee, Wonwoo [Sogang University, Center for Quantum Spacetime, Seoul (Korea, Republic of); Lee, Bum-Hoon [Sogang University, Center for Quantum Spacetime, Seoul (Korea, Republic of); Sogang University, Department of Physics, Seoul (Korea, Republic of); Asia Pacific Center for Theoretical Physics, Pohang (Korea, Republic of)
2015-08-15
We investigate the fragmentation instability of hairy black holes in the theory with a Gauss-Bonnet (GB) term in asymptotically flat spacetime. Our approach is through the non-perturbative fragmentation instability. By this approach, we investigate whether the initial black hole can be broken into two black holes by comparing the entropy of the initial black hole with the sum of those of two fragmented black holes. The relation between the black hole instability and the GB coupling with dilaton hair are presented. We describe the phase diagrams with respect to the mass of the black hole solutions and coupling constants. We find that a perturbatively stable black hole can be unstable under fragmentation. (orig.)
Instability of black holes with a Gauss-Bonnet term
International Nuclear Information System (INIS)
We investigate the fragmentation instability of hairy black holes in the theory with a Gauss-Bonnet (GB) term in asymptotically flat spacetime. Our approach is through the non-perturbative fragmentation instability. By this approach, we investigate whether the initial black hole can be broken into two black holes by comparing the entropy of the initial black hole with the sum of those of two fragmented black holes. The relation between the black hole instability and the GB coupling with dilaton hair are presented. We describe the phase diagrams with respect to the mass of the black hole solutions and coupling constants. We find that a perturbatively stable black hole can be unstable under fragmentation. (orig.)
Evaporation of a black hole off of a tense brane
International Nuclear Information System (INIS)
We calculate the greybody factors for scalar, vector and graviton fields in the background of an exact black hole localized on a tensional 3-brane in a world with two large extra dimensions. Finite brane tension modifies the standard results for the case with of a black hole on a brane with negligible tension. For a black hole of a fixed mass, the power carried away into the bulk diminishes as the tension increases, because the effective Planck constant, and therefore entropy of a fixed mass black hole, increase. In this limit, the semiclassical description of black hole decay becomes more reliable
Attractor black holes and quantum distribution functions
Energy Technology Data Exchange (ETDEWEB)
Montanez, S. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Gomez, C. [Instituto de Fisica Teorica CSIC-UAM, Modulo C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain); Theory Group, Physics Department, CERN, 1211 Geneva 23 (Switzerland)
2007-05-15
Using the attractor mechanism and the wavefunction interpretation of the topological string partition function on a Calabi Yau threefold M we study the relation between the Bekenstein-Hawking-Wald entropy of BPS Calabi-Yau black holes and quantum distribution functions defined on H{sup 3}(M). We discuss the OSV conjecture in this context. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
International Nuclear Information System (INIS)
The 'no-hair' theorem, a key result in general relativity, states that an isolated black hole is defined by only three parameters: mass, angular momentum, and electric charge; this asymptotic state is reached on a light-crossing time scale. We find that the no-hair theorem is not formally applicable for black holes formed from the collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively ''frozen in'' the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tubes NB=eΦ∞/(πc(ℎ/2π)), where Φ∞≅2π2BNSRNS3/(PNSc) is the initial magnetic flux through the hemispheres of the progenitor and out to infinity. We test this theoretical result via 3-dimensional general relativistic plasma simulations of rotating black holes that start with a neutron star dipole magnetic field with no currents initially present outside the event horizon. The black hole's magnetosphere subsequently relaxes to the split-monopole magnetic field geometry with self-generated currents outside the event horizon. The dissipation of the resulting equatorial current sheet leads to a slow loss of the anchored flux tubes, a process that balds the black hole on long resistive time scales rather than the short light-crossing time scales expected from the vacuum no-hair theorem.
Good, Michael R R
2014-01-01
A $(3+1)$-dimensional asymptotically flat Kerr black hole angular speed $\\Omega_+$ can be used to define an effective spring constant, $k=m\\Omega_+^2$. Its maximum value is the Schwarzschild surface gravity, $k = \\kappa $, which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature is expressed in terms of the spring constant: $2\\pi T = \\kappa - k$. Hooke's law, in the extremal limit, provides the force $F = 1/4$, which is consistent with the conjecture of maximum force in general relativity.
Noncommutative solitonic black hole
International Nuclear Information System (INIS)
We investigate solitonic black hole solutions in three-dimensional noncommutative spacetime. We do this in gravity with a negative cosmological constant coupled to a scalar field. Noncommutativity is realized with the Moyal product which is expanded up to first order in the noncommutativity parameter in two spatial directions. With numerical simulation we study the effect of noncommutativity by increasing the value of the noncommutativity parameter starting from commutative solutions. We find that even a regular soliton solution in the commutative case becomes a black hole solution when the noncommutativity parameter reaches a certain value. (paper)
Noncommutative solitonic black hole
Chang-Young, Ee; Kimm, Kyoungtae; Lee, Daeho; Lee, Youngone
2012-05-01
We investigate solitonic black hole solutions in three-dimensional noncommutative spacetime. We do this in gravity with a negative cosmological constant coupled to a scalar field. Noncommutativity is realized with the Moyal product which is expanded up to first order in the noncommutativity parameter in two spatial directions. With numerical simulation we study the effect of noncommutativity by increasing the value of the noncommutativity parameter starting from commutative solutions. We find that even a regular soliton solution in the commutative case becomes a black hole solution when the noncommutativity parameter reaches a certain value.
Horndeski black hole geodesics
Tretyakova, D A
2016-01-01
We examine geodesics for the scalar-tensor black holes in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits may not be present within some model parameters range. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations. We also present a new (although very similar to those previously known) solution, which contains the orbits we expect from a compact object, admits regular scalar field at the horizon and and can fit into the known stability criteria.
Aarseth, Sverre J
2007-01-01
We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic Regularization. These methods have been tried out with some success on GRAPE-type computers. Special emphasis has also been devoted to including post-Newtonian terms, with application to moderately massive black holes in stellar clusters. Some examples of simulations leading to coalescence by gravitational radiation will be presented to illustrate the practical usefulness of such methods.
Modeling black hole evaporation
Fabbri, Alessandro
2005-01-01
The scope of this book is two-fold: the first part gives a fully detailed and pedagogical presentation of the Hawking effect and its physical implications, and the second discusses the backreaction problem, especially in connection with exactly solvable semiclassical models that describe analytically the black hole evaporation process. The book aims to establish a link between the general relativistic viewpoint on black hole evaporation and the new CFT-type approaches to the subject. The detailed discussion on backreaction effects is also extremely valuable.
Hennigar, Robie A; Tjoa, Erickson
2016-01-01
We present what we believe is the first example of a "$\\lambda$-line" phase transition in black hole thermodynamics. This is a line of (continuous) second order phase transitions which in the case of liquid $^4$He marks the onset of superfluidity. The phase transition occurs for a class of asymptotically AdS hairy black holes in Lovelock gravity where a real scalar field is conformally coupled to gravity. We discuss the origin of this phase transition and outline the circumstances under which it (or generalizations of it) could occur.
Superconformal Quantum Mechanics of Small Black Holes
Kim, S; Kim, Seok; Raeymaekers, Joris
2005-01-01
Recently, Gaiotto, Strominger and Yin have proposed a holographic dual description for the near-horizon physics of certain N=2 black holes in terms of the superconformal quantum mechanics on D0-branes in the attractor geometry. We provide further evidence for their proposal by applying it to the case of `small' black holes which have vanishing horizon area in the leading supergravity approximation. We consider 2-charge black holes in type IIA on $T^2 \\times M$, where $M$ can be either $K_3$ or $T^4$, made up out of D0-branes and D4-branes wrapping $M$. We construct the corresponding superconformal quantum mechanics and show that the asymptotic growth of chiral primaries exactly matches with the known entropy of these black holes. The state-counting problem reduces to counting lowest Landau levels on $T^2$ and Dolbeault cohomology classes on $M$.
Institute of Scientific and Technical Information of China (English)
邓昭镜
2012-01-01
试探地通过相空间理论计算稳定黑洞在其形成过程中相体积的变化来直接分析黑洞在其形成过程中熵的演化.结果发现,按照这一思路能有效地研究黑洞形成过程中的熵演化规律.%In this paper, the changes in phase volume during the formation of stationary black holes are calculated, using the theory of phase space, so as to analyze the entropy evolution in the process of their formation. We find that this approach is helpful for the study of the evolution of entropy of black holes during their formation.
Lyutikov, Maxim; McKinney, Jonathan C.
2011-10-01
The “no-hair” theorem, a key result in general relativity, states that an isolated black hole is defined by only three parameters: mass, angular momentum, and electric charge; this asymptotic state is reached on a light-crossing time scale. We find that the no-hair theorem is not formally applicable for black holes formed from the collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively “frozen in” the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tubes NB=eΦ∞/(πcℏ), where Φ∞≈2π2BNSRNS3/(PNSc) is the initial magnetic flux through the hemispheres of the progenitor and out to infinity. We test this theoretical result via 3-dimensional general relativistic plasma simulations of rotating black holes that start with a neutron star dipole magnetic field with no currents initially present outside the event horizon. The black hole’s magnetosphere subsequently relaxes to the split-monopole magnetic field geometry with self-generated currents outside the event horizon. The dissipation of the resulting equatorial current sheet leads to a slow loss of the anchored flux tubes, a process that balds the black hole on long resistive time scales rather than the short light-crossing time scales expected from the vacuum no-hair theorem.
Horowitz, Gary T.; Maldacena, Juan
2003-01-01
We propose that in quantum gravity one needs to impose a final state boundary condition at black hole singularities. This resolves the apparent contradiction between string theory and semiclassical arguments over whether black hole evaporation is unitary.
Quantum aspects of black holes
2015-01-01
Beginning with an overview of the theory of black holes by the editor, this book presents a collection of ten chapters by leading physicists dealing with the variety of quantum mechanical and quantum gravitational effects pertinent to black holes. The contributions address topics such as Hawking radiation, the thermodynamics of black holes, the information paradox and firewalls, Monsters, primordial black holes, self-gravitating Bose-Einstein condensates, the formation of small black holes in high energetic collisions of particles, minimal length effects in black holes and small black holes at the Large Hadron Collider. Viewed as a whole the collection provides stimulating reading for researchers and graduate students seeking a summary of the quantum features of black holes.
Energy Technology Data Exchange (ETDEWEB)
Bouhmadi-Lopez, Mariam; Cardoso, Vitor; Nerozzi, Andrea; Rocha, Jorge V, E-mail: mariam.bouhmadi@ist.utl.pt, E-mail: vitor.cardoso@ist.utl.pt, E-mail: andrea.nerozzi@ist.utl.pt, E-mail: jorge.v.rocha@ist.utl.pt [CENTRA, Department de Fisica, Instituto Superior Tecnico, Av. Rovisco Pais 1, 1049 Lisboa (Portugal)
2011-09-22
A possible process to destroy a black hole consists on throwing point particles with sufficiently large angular momentum into the black hole. In the case of Kerr black holes, it was shown by Wald that particles with dangerously large angular momentum are simply not captured by the hole, and thus the event horizon is not destroyed. Here we reconsider this gedanken experiment for black holes in higher dimensions. We show that this particular way of destroying a black hole does not succeed and that Cosmic Censorship is preserved.
Growth of Primordial Black Holes
Harada, Tomohiro
Primordial black holes have important observational implications through Hawking evaporation and gravitational radiation as well as being a candidate for cold dark matter. Those black holes are assumed to have formed in the early universe typically with the mass scale contained within the Hubble horizon at the formation epoch and subsequently accreted mass surrounding them. Numerical relativity simulation shows that primordial black holes of different masses do not accrete much, which contrasts with a simplistic Newtonian argument. We see that primordial black holes larger than the 'super-horizon' primordial black holes have decreasing energy and worm-hole like struture, suggesting the formation through quamtum processes.
Black Hole Evaporation. A Survey
Benachenhou, Farid
1994-01-01
This thesis is a review of black hole evaporation with emphasis on recent results obtained for two dimensional black holes. First, the geometry of the most general stationary black hole in four dimensions is described and some classical quantities are defined. Then, a derivation of the spectrum of the radiation emitted during the evaporation is presented. In section four, a two dimensional model which has black hole solutions is introduced, the so-called CGHS model. These two dimensional blac...
Black Hole: The Interior Spacetime
Ong, Yen Chin
2016-01-01
The information loss paradox is often discussed from the perspective of the observers who stay outside of a black hole. However, the interior spacetime of a black hole can be rather nontrivial. We discuss the open problems regarding the volume of a black hole, and whether it plays any role in information storage. We also emphasize the importance of resolving the black hole singularity, if one were to resolve the information loss paradox.
Thermodynamic product formula for a Taub-NUT black hole
Pradhan, P.
2016-01-01
We derive various important thermodynamic relations of the inner and outer horizons in the background of the Taub-NUT (Newman-Unti-Tamburino) black hole in four-dimensional Lorentzian geometry. We compare these properties with the properties of the Reissner-Nordström black hole. We compute the area product, area sum, area subtraction, and area division of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From the area bound, we derive an entropy bound and an irreducible mass bound for both horizons. We further study the stability of such black holes by computing the specific heat for both horizons. It is shown that due to the negative specific heat, the black hole is thermodynamically unstable. All these calculations might be helpful in understanding the nature of the black hole entropy (both interior and exterior) at the microscopic level.
Thermodynamic Product Formula for Taub-NUT Black Hole
Pradhan, Parthapratim
2016-01-01
We derive various important thermodynamic relations of the inner and outer horizon in the background of Taub-NUT(Newman-Unti-Tamburino) black hole in four dimensional \\emph{Lorentzian geometry}. We compare these properties with the properties of Reissner Nordstr{\\o}m black hole. We compute \\emph{area product, area sum, area minus and area division} of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From area bound, we derive entropy bound and irreducible mass bound for both the horizons. We further study the stability of such black hole by computing the specific heat for both the horizons. It is shown that due to negative specific heat the black hole is thermodynamically unstable. All these calculations might be helpful to understanding the nature of black hole entropy both \\emph{interior} and exterior at the microscopic level.
Connecting horizon pixels and interior voxels of a black hole
Nicolini, Piero
2014-01-01
In this paper we discuss to what extent one can infer details of the interior structure of a black hole based on its horizon. Recalling that black hole thermal properties are connected to the non-classical nature of gravity, we circumvent the restrictions of the no hair theorem by postulating that the black hole interior is singularity free due to violations of the usual energy conditions. Further these conditions allow one to establish a one-to-one, holographic projection between Planckian areal "bits" on the horizon and "voxels", representing the gravitational degrees of freedom in the black hole interior. We illustrate the repercussions of this idea by discussing an example of the black hole interior consisting of a de Sitter core postulated to arise from the local graviton quantum vacuum energy. It is shown that the black hole entropy can emerge as the statistical entropy of a gas of voxels.
Connecting horizon pixels and interior voxels of a black hole
International Nuclear Information System (INIS)
In this paper we discuss to what extent one can infer details of the interior structure of a black hole based on its horizon. Recalling that black hole thermal properties are connected to the non-classical nature of gravity, we circumvent the restrictions of the no-hair theorem by postulating that the black hole interior is singularity free due to violations of the usual energy conditions. Further these conditions allow one to establish a one-to-one, holographic projection between Planckian areal “bits” on the horizon and “voxels”, representing the gravitational degrees of freedom in the black hole interior. We illustrate the repercussions of this idea by discussing an example of the black hole interior consisting of a de Sitter core postulated to arise from the local graviton quantum vacuum energy. It is shown that the black hole entropy can emerge as the statistical entropy of a gas of voxels
Duff, M J
2012-01-01
Quantum entanglement lies at the heart of quantum information theory, with applications to quantum computing, teleportation, cryptography and communication. In the apparently separate world of quantum gravity, the Hawking effect of radiating black holes has also occupied centre stage. Despite their apparent differences, it turns out that there is a correspondence between the two.
Energy Technology Data Exchange (ETDEWEB)
Bambi, Cosimo, E-mail: bambi@fudan.edu.cn; Modesto, Leonardo, E-mail: lmodesto@fudan.edu.cn
2013-04-25
The formation of spacetime singularities is a quite common phenomenon in General Relativity and it is regulated by specific theorems. It is widely believed that spacetime singularities do not exist in Nature, but that they represent a limitation of the classical theory. While we do not yet have any solid theory of quantum gravity, toy models of black hole solutions without singularities have been proposed. So far, there are only non-rotating regular black holes in the literature. These metrics can be hardly tested by astrophysical observations, as the black hole spin plays a fundamental role in any astrophysical process. In this Letter, we apply the Newman–Janis algorithm to the Hayward and to the Bardeen black hole metrics. In both cases, we obtain a family of rotating solutions. Every solution corresponds to a different matter configuration. Each family has one solution with special properties, which can be written in Kerr-like form in Boyer–Lindquist coordinates. These special solutions are of Petrov type D, they are singularity free, but they violate the weak energy condition for a non-vanishing spin and their curvature invariants have different values at r=0 depending on the way one approaches the origin. We propose a natural prescription to have rotating solutions with a minimal violation of the weak energy condition and without the questionable property of the curvature invariants at the origin.
Baker, John
2010-01-01
Among the fascinating phenomena predicted by General Relativity, Einstein's theory of gravity, black holes and gravitational waves, are particularly important in astronomy. Though once viewed as a mathematical oddity, black holes are now recognized as the central engines of many of astronomy's most energetic cataclysms. Gravitational waves, though weakly interacting with ordinary matter, may be observed with new gravitational wave telescopes, opening a new window to the universe. These observations promise a direct view of the strong gravitational dynamics involving dense, often dark objects, such as black holes. The most powerful of these events may be merger of two colliding black holes. Though dark, these mergers may briefly release more energy that all the stars in the visible universe, in gravitational waves. General relativity makes precise predictions for the gravitational-wave signatures of these events, predictions which we can now calculate with the aid of supercomputer simulations. These results provide a foundation for interpreting expect observations in the emerging field of gravitational wave astronomy.
Energy Technology Data Exchange (ETDEWEB)
Bender, P. [Univ. of Colorado, Boulder, CO (United States); Bloom, E. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Cominsky, L. [Sonoma State Univ., Rohnert Park, CA (United States). Dept. of Physics and Astronomy] [and others
1995-07-01
Black-hole astrophysics is not just the investigation of yet another, even if extremely remarkable type of celestial body, but a test of the correctness of the understanding of the very properties of space and time in very strong gravitational fields. Physicists` excitement at this new prospect for testing theories of fundamental processes is matched by that of astronomers at the possibility to discover and study a new and dramatically different kind of astronomical object. Here the authors review the currently known ways that black holes can be identified by their effects on their neighborhood--since, of course, the hole itself does not yield any direct evidence of its existence or information about its properties. The two most important empirical considerations are determination of masses, or lower limits thereof, of unseen companions in binary star systems, and measurement of luminosity fluctuations on very short time scales.
Asymptotically Lifshitz brane-world black holes
International Nuclear Information System (INIS)
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: ► Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. ► Studying the thermodynamical behavior of asymptotically Lifshitz black holes. ► Showing that the entropy imposes the critical exponent z to be bounded from above. ► Discussing the phase transition for different spatial topologies.
Warped products and black holes
International Nuclear Information System (INIS)
We apply the warped product space-time scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordstroem-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes
Warped products and black holes
Hong, S T
2005-01-01
We apply the warped product spacetime scheme to the Banados-Teitelboim-Zanelli black holes and the Reissner-Nordstr\\"om-anti-de Sitter black hole to investigate their interior solutions in terms of warped products. It is shown that there exist no discontinuities of the Ricci and Einstein curvatures across event horizons of these black holes.
Black Holes in Higher Dimensions
International Nuclear Information System (INIS)
In four space-time dimensions black holes of Einstein-Maxwell theory satisfy a number of theorems. In more than four space-time dimensions, however, some of the properties of black holes can change. In particular, uniqueness of black holes no longer holds. In five and more dimensions black rings arise. Thus in a certain region of the phase diagram there are three black objects with the same global charges present. Here we discuss properties of higher-dimensional vacuum and charged black holes, which possess a spherical horizon topology, and of vacuum and charged black rings, which have a ringlike horizon topology
星系内黑洞形成过程的熵演化%The Evolution of Entropy in the Process of Black Hole Formation in Nebulae/Galaxies
Institute of Scientific and Technical Information of China (English)
邓昭镜; 陈华林
2012-01-01
In this paper, the process of black hole formation in nebulae is divided into two stages (phases), one is called "arrangement process" and the other is called "impact radiation process". A detailed analysis is given of the evolution of the entropy of nebula (or the broad-sense entropy of black hole) at the two phases from the respect of the thermodynamics, the gravitational field and the quantum radiation. It is concluded that the process of the formation of any black hole in the nebula is an entropy-decrease process.%将星系中黑洞的形成过程分为两个阶段:第一个阶段是有序化的“整肃”阶段,第二个阶段是无序化的“撞击”阶段.从热力学角度和引力场论、量子辐射的角度详细地分析了这两个阶段中星系系统熵(黑洞广义熵)的演化,得出星系中黑洞的形成过程是一个熵减少过程的结论.
N=2 Extremal Black Holes and Intersecting Branes
Maldacena, Juan M.
1996-01-01
Using a simple hypothesis about the degrees of freedom of intersecting branes we find a microscopic counting argument that reproduces the entropy of a class of BPS black holes of type IIA string theory on general Calabi Yau three folds.
Kerr black hole in canonically deformed space-time
Daszkiewicz, Marcin
2014-01-01
We investigate the Kerr black hole defined on canonically deformed space-time. Particulary, we find the corresponding event horizon, the ergosphere, the temperature and the entropy of such deformed object.
Black hole thermalization rate from brane anti-brane model
Lifschytz, G
2004-01-01
We develop the quasi-particle picture for Schwarzchild and far from extremal black holes. We show that the thermalization equations of the black hole is recovered from the model of branes and anti-branes. This can also be viewed as a field theory explanation of the relationship between area and entropy for these black holes. As a by product the annihilation rate of branes and anti-branes is computed.
Black hole thermalization rate from brane anti-brane model
Energy Technology Data Exchange (ETDEWEB)
Lifschytz, Gilad E-mail: giladl@research.haifa.ac.il
2004-08-01
We develop the quasi-particle picture for Schwarzchild and far from extremal black holes. We show that the thermalization equations of the black hole is recovered from the model of branes and anti-branes. This can also be viewed as a field theory explanation of the relationship between area and entropy for these black holes. As a by product the annihilation rate of branes and anti-branes is computed. (author)
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
Tunnelling effect of the non-stationary Kerr black hole
Yang, Shu-Zheng; Chen, De-You
2008-03-01
Extending Parikh and Wilczek's work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilton-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein-Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.
Tunnelling effect of the non-stationary Kerr black hole
Institute of Scientific and Technical Information of China (English)
Yang Shu-Zheng; Chen De-You
2008-01-01
Extending Parikh and Wilezek's work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilton-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein-Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.
Noncommutative geometry-inspired rotating black hole in three dimensions
Indian Academy of Sciences (India)
Juan Manuel Tejeiro; Alexis Larrañaga
2012-01-01
We ﬁnd a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect ﬂuid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution and give corrections to the area law to get the exact nature of the Bekenstein–Hawking entropy.
Quasinormal spectrum and the black hole membrane paradigm
Starinets, A. O.
2008-01-01
The membrane paradigm approach to black hole physics introduces the notion of a stretched horizon as a fictitious time-like surface endowed with physical characteristics such as entropy, viscosity and electrical conductivity. We show that certain properties of the stretched horizons are encoded in the quasinormal spectrum of black holes. We compute analytically the lowest quasinormal frequency of a vector-type perturbation for a generic black hole with a translationally invariant horizon (bla...
Black hole at Lovelock gravity with anisotropic fluid
Aros, Rodrigo; Estrada, Milko; Montecinos, Alejandra
2016-01-01
In this work a new family of black hole solutions in Lovelock gravity is discussed. These solutions describe anisotropic fluids which extend to the spatial infinity. Though far from the horizon their geometries approach some previously known black holes solutions the location of the horizons differ. Furthemore, although the masses of these solutions match the masses of those previously known black holes, their temperatures and entropies differ.
Black Hole Thermodynamics from a Noncommutative Area Operator
Pérez-Payán, S.; Sabido, M.
2012-01-01
One key element to calculate thermodynamical properties for a black hole is the partition function. In this paper we have incorporated the idea of a two dimensional area in a noncommutative space and were able to calculate the partition function with such a spectra. Employing the canonical quantum statistics formalism we compute the temperature, entropy and time of evaporation for a Schwarzschild black hole.
Thermodynamics of the Schwarzschild Black Hole in Noncommutative Space
International Nuclear Information System (INIS)
In this paper we study noncommutative black holes. In particular, we use a deform Schwarzschild solution in noncommutative gauge theory of gravity. By means of euclidean quantum gravity we obtain the entropy, temperatute and the time of evaporation of the noncommutative black hole.
Black Hole Statistical Mechanics and The Angular Velocity Ensemble
Thomson, Mitchell
2012-01-01
An new ensemble - the angular velocity ensemble - is derived using Jaynes' method of maximising entropy subject to prior information constraints. The relevance of the ensemble to black holes is motivated by a discussion of external parameters in statistical mechanics and their absence from the Hamiltonian of general relativity. It is shown how this leads to difficulty in deriving entropy as a function of state and recovering the first law of thermodynamics from the microcanonical and canonical ensembles applied to black holes.
Observational Evidence for Black Holes
Narayan, Ramesh; McClintock, Jeffrey E.
2013-01-01
Astronomers have discovered two populations of black holes: (i) stellar-mass black holes with masses in the range 5 to 30 solar masses, millions of which are present in each galaxy in the universe, and (ii) supermassive black holes with masses in the range 10^6 to 10^{10} solar masses, one each in the nucleus of every galaxy. There is strong circumstantial evidence that all these objects are true black holes with event horizons. The measured masses of supermassive black hole are strongly corr...
Black holes as collapsed polymers
Brustein, Ram
2016-01-01
We propose that a large Schwarzschild black hole (BH) is a bound state of highly excited, long, closed strings at the Hagedorn temperature. The size of the bound state is smaller than the string random-walk scale and determined dynamically by the string attractive interactions. It is further proposed that the effective free-energy density of the bound state should be expressed as a function of its entropy density. For a macroscopic BH, the free-energy density contains only linear and quadratic terms, in analogy with that of a collapsed polymer when expressed as a function of the polymer concentration. Using the effective free energy, we derive scaling relations for the entropy, energy and size of the bound state and show that these agree with the scaling relations of the BH; in particular, with the area law for the BH entropy. The area law originates from the inverse scaling of the effective temperature with the bound-state radius. We also find that the energy density of the bound state is equal to its pressu...
Prisons of light : black holes
Ferguson, Kitty
What is a black hole? Could we survive a visit to one -- perhaps even venture inside? Have we yet discovered any real black holes? And what do black holes teach us about the mysteries of our Universe? These are just a few of the tantalizing questions examined in this tour-de-force, jargon-free review of one of the most fascinating topics in modern science. In search of the answers, we trace a star from its birth to its death throes, take a hypothetical journey to the border of a black hole and beyond, spend time with some of the world's leading theoretical physicists and astronomers, and take a whimsical look at some of the wild ideas black holes have inspired. Prisons of Light - Black Holes is comprehensive and detailed. Yet Kitty Ferguson's lightness of touch and down-to-earth analogies set this book apart from all others on black holes and make it a wonderfully stimulating and entertaining read.
Point mass Cosmological Black Holes
Firouzjaee, Javad T
2016-01-01
Real black holes in the universe are located in the expanding accelerating background which are called the cosmological black holes. Hence, it is necessary to model these black holes in the cosmological background where the dark energy is the dominant energy. In this paper, we argue that most of the dynamical cosmological black holes can be modeled by point mass cosmological black holes. Considering the de Sitter background for the accelerating universe, we present the point mass cosmological background in the cosmological de Sitter space time. Our work also includes the point mass black holes which have charge and angular momentum. We study the mass, horizons, redshift structure and geodesics properties for these black holes.
Philosophical Issues of Black Holes
Romero, Gustavo E
2014-01-01
Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermodynamics and its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinisim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology.
Brick Walls for Nonstationary Black Holes
Institute of Scientific and Technical Information of China (English)
黎忠恒; 米丽琴; 赵峥
2002-01-01
The validity condition of the brick-wall model is analysed in nonstationary space time. It is shown that the model holds only in thin regions, only by using tortoise coordinates, near the event horizon of a slowly varying (quasi-stationary) black hole. The reason for the use of tortoise coordinates is that the stationary state solutions of quantum field equations in other coordinates do not exist for any region in nonstationary space-time. Meanwhile,the quantum corrections to the entropy of the Vaidya-Bonner black hole due to the spin fields are calculated in terms of the brick-wall model.
Entropic gravity from noncommutative black holes
Nunes, Rafael C; Barboza, Edésio M; Abreu, Everton M C; Neto, Jorge Ananias
2016-01-01
In this paper we will investigate the effects of a noncommutative (NC) space-time on the dynamics of the universe. We will generalize the black hole entropy formula for a NC black hole. Then, using the entropic gravity formalism, we will show that the noncommutativity changes the strength of the gravitational field. By applying this result to a homogeneous and isotropic universe containing nonrelativistic matter and a cosmological constant, we will show that the model modified by the noncommutativity of the space-time is a better fit to the obtained data than the standard one.
Diagonalizing the Black Hole Information Retrieval Process
Hooft, Gerard t
2015-01-01
The mechanism by which black holes return the absorbed information to the outside world is reconsidered, and described in terms of a set of mutually non-interacting modes. Our mechanism is based on the mostly classical gravitational back-reaction. The diagonalized formalism is particularly useful for further studies of this process. Although no use is made of string theory, our analysis appears to point towards an ensuing string-like interaction. It is shown how black hole entropy can be traced down to classical gravitational back-reaction.
Tensor network and a black hole
Matsueda, Hiroaki; Ishihara, Masafumi; Hashizume, Yoichiro
2013-03-01
A tensor-network variational formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, a multiscale entanglement renormalization ansatz reproduces an anti-de Sitter black hole at finite temperature. Our finding shows rich functionalities of multiscale entanglement renormalization ansatz as efficient graphical representation of AdS/CFT correspondence.
Bena, Iosif; Vercnocke, Bert
2012-01-01
We establish the relation between the structure governing supersymmetric and non-supersymmetric four- and five-dimensional black holes and multicenter solutions and Calabi-Yau flux compactifications of M-theory and type IIB string theory. We find that the known BPS and almost-BPS multicenter black hole solutions can be interpreted as GKP compactifications with (2,1) and (0,3) imaginary self-dual flux. We also show that the most general GKP compactification leads to new classes of BPS and non-BPS multicenter solutions. We explore how these solutions fit into N=2 truncations, and elucidate how supersymmetry becomes camouflaged. As a necessary tool in our exploration we show how the fields in the largest N=2 truncation fit inside the six-torus compactification of eleven-dimensional supergravity.
Clement, María E Gabach
2015-01-01
It is well known that celestial bodies tend to be spherical due to gravity and that rotation produces deviations from this sphericity. We discuss what is known and expected about the shape of black holes' horizons from their formation to their final, stationary state. We present some recent results showing that black hole rotation indeed manifests in the widening of their central regions, limits their global shapes and enforces their whole geometry to be close to the extreme Kerr horizon geometry at almost maximal rotation speed. The results depend only on the horizon area and angular momentum. In particular they are entirely independent of the surrounding geometry of the spacetime and of the presence of matter satisfying the strong energy condition. We also discuss the the relation of this result with the Hoop conjecture.
Romero, Gustavo E
2014-01-01
Presentism is, roughly, the metaphysical doctrine that maintains that whatever exists, exists in the present. The compatibility of presentism with the theories of special and general relativity was much debated in recent years. It has been argued that at least some versions of presentism are consistent with time-orientable models of general relativity. In this paper we confront the thesis of presentism with relativistic physics, in the strong gravitational limit where black holes are formed. We conclude that the presentist position is at odds with the existence of black holes and other compact objects in the universe. A revision of the thesis is necessary, if it is intended to be consistent with the current scientific view of the universe.
Polchinski, Joseph
2015-04-01
Our modern understanding of space, time, matter, and even reality itself arose from the three great revolutions of the early twentieth century: special relativity, general relativity, and quantum mechanics. But a century later, this work is unfinished. Many deep connections have been discovered, but the full form of a unified theory incorporating all three principles is not known. Thought experiments and paradoxes have often played a key role in figuring out how to fit theories together. For the unification of general relativity and quantum mechanics, black holes have been an important arena. I will talk about the quantum mechanics of black holes, the information paradox, and the latest version of this paradox, the firewall. The firewall points to a conflict between our current theories of spacetime and of quantum mechanics. It may lead to a new understanding of how these are connected, perhaps based on quantum entanglement.
Black Hole Thermodynamics from the point of view of Superstring Theory
Akhmedov, E. T.
1997-01-01
In this review we try to give a pedagogical introduction to the recent progress in the resolution of old problems of black hole thermodynamics within superstring theory. We start with a brief description of classical black hole dynamics. Then, follow with the consideration of general properties of supersymmetric black holes. We conclude with the review of the statistical explanation of the black hole entropy and string theory description of the black hole evaporation.
Black Holes in Higher Dimensions
Directory of Open Access Journals (Sweden)
Reall Harvey S.
2008-09-01
Full Text Available We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers–Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.
Black holes as bubble nucleation sites
International Nuclear Information System (INIS)
We consider the effect of inhomogeneities on the rate of false vacuum decay. Modelling the inhomogeneity by a black hole, we construct explicit Euclidean instantons which describe the nucleation of a bubble of true vacuum centred on the inhomogeneity. We find that inhomogeneity significantly enhances the nucleation rate over that of the Coleman-de Luccia instanton — the black hole acts as a nucleation site for the bubble. The effect is larger than previously believed due to the contributions to the action from conical singularities. For a sufficiently low initial mass, the original black hole is replaced by flat space during this process, as viewed by a single causal patch observer. Increasing the initial mass, we find a critical value above which a black hole remnant survives the process. This resulting black hole can have a higher mass than the original black hole, but always has a lower entropy. We compare the process to bubble-to-bubble transitions, where there is a semi-classical Lorentzian description in the WKB approximation
Noncommutative Solitonic Black Hole
Chang-Young, Ee; Kimm, Kyoungtae; Lee, Daeho; Lee, Youngone
2011-01-01
We investigate solitonic black hole solutions in three dimensional noncommutative spacetime. We do this in gravity with negative cosmological constant coupled to a scalar field. Noncommutativity is realized with the Moyal product which is expanded up to first order in the noncommutativity parameter in two spatial directions. With numerical simulation we study the effect of noncommutativity by increasing the value of the noncommutativity parameter starting from commutative solutions. We find t...
Lyutikov, Maxim
2011-01-01
The "no hair" theorem, a key result in General Relativity, states that an isolated black hole is defined by only three parameters: mass, angular momentum, and electric charge; this asymptotic state is reached on a light-crossing time scale. We find that the "no hair" theorem is not formally applicable for black holes formed from collapse of a rotating neutron star. Rotating neutron stars can self-produce particles via vacuum breakdown forming a highly conducting plasma magnetosphere such that magnetic field lines are effectively "frozen-in" the star both before and during collapse. In the limit of no resistivity, this introduces a topological constraint which prohibits the magnetic field from sliding off the newly-formed event horizon. As a result, during collapse of a neutron star into a black hole, the latter conserves the number of magnetic flux tubes $N_B = e \\Phi_\\infty /(\\pi c \\hbar)$, where $\\Phi_\\infty \\approx 2 \\pi^2 B_{NS} R_{NS}^3 /(P_{\\rm NS} c)$ is the initial magnetic flux through the hemisphere...
Asymptotically Lifshitz brane-world black holes
Energy Technology Data Exchange (ETDEWEB)
Ranjbar, Arash, E-mail: a_ranjbar@sbu.ac.ir; Sepangi, Hamid Reza, E-mail: hr-sepangi@sbu.ac.ir; Shahidi, Shahab, E-mail: s_shahidi@sbu.ac.ir
2012-12-15
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the thermodynamical behavior of such asymptotically Lifshitz black holes. It is shown that the entropy imposes the critical exponent z to be bounded from above. This maximum value of z corresponds to a positive infinite entropy as long as the temperature is kept positive. The stability and phase transition for different spatial topologies are also discussed. - Highlights: Black-Right-Pointing-Pointer Studying the gravity dual of a Lifshitz field theory in the context of brane-world scenario. Black-Right-Pointing-Pointer Studying the thermodynamical behavior of asymptotically Lifshitz black holes. Black-Right-Pointing-Pointer Showing that the entropy imposes the critical exponent z to be bounded from above. Black-Right-Pointing-Pointer Discussing the phase transition for different spatial topologies.