P. Mitra
1994-01-01
In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy $S^{BH}$ (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy $S^{SM}=-\\mbox{Tr}(\\hat{\\rho}\\ln \\hat{\\rho})$ (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (...
Frolov, V
1994-01-01
In the talk different definitions of the black hole entropy are discussed and compared. It is shown that the Bekenstein-Hawking entropy S^{BH} (defined by the response of the free energy of a system containing a black hole on the change of the temperature) differs from the statistical- mechanical entropy S^{SM}=-\\mbox{Tr}(\\hat{\\rho}\\ln \\hat{\\rho}) (defined by counting internal degrees of freedom of a black hole). A simple explanation of the universality of the Bekenstein-Hawking entropy (i.e. its independence of the number and properties of the fields which might contribute to S^{SM}) is given.
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.
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.
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.
General Logarithmic Corrections to Black Hole Entropy
Das, S; Bhaduri, R K; Das, Saurya; Majumdar, Parthasarathi; Bhaduri, Rajat K.
2002-01-01
We compute leading order corrections to the the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form $-k\\ln(Area)$. For BTZ black holes, $k=3/2$, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner-Nordstrom black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black hole entropy and its corrections.
Tachyon condensation and black hole entropy.
Dabholkar, Atish
2002-03-04
String propagation on a cone with deficit angle 2pi(1-1 / N) is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.
Entropy and temperatures of Nariai black hole
Eune, Myungseok; Kim, Wontae
2013-06-01
The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the timelike Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.
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 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
An Exact Black Hole Entropy Bound
Birmingham, Daniel; Birmingham, Danny; Sen, Siddhartha
2001-01-01
We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.
Black hole entropy without brick walls
Xiang, Li
2002-01-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzshild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportiona...
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.
Entropy and temperatures of Nariai black hole
Eune, Myungseok; Kim, Wontae
2012-01-01
The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick-wall method. Even if the temperature depends on the choice of the time-like Killing vector, the entropy can be written by the ordinary area law which agrees with the Wald entropy. We discuss some physical consequences of this result and the properties of the temperatures.
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.
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.
A Note on Entropy Relations of Black Hole Horizons
Meng, Xin-he; Xu, Wei; WANG Jia
2014-01-01
We focus on the entropy relations of black holes in three, four and higher dimensions. These entropy relations include entropy product, "part" entropy product and entropy sum. We also discuss their differences and similarities, in order to make a further study on understanding the origin of black hole entropy at the microscopic level.
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.
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.
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 without brick walls
Xiang, L
2002-01-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzshild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Black hole entropy without brick walls
Xiang, Li
2002-07-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of a Schwarzschild black hole. When the new equation of state density is utilized to investigate the entropy of a scalar field outside the horizon of a static black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Rotating embedded black holes: Entropy and Hawking's radiation
2004-01-01
In this paper we derive a class of rotating embedded black holes. Then we study Hawking's radiation effects on these embedded black holes. The surface gravity, entropy and angular velocity are given for each of these black holes.
Hawking radiation without black hole entropy
Visser, M
1998-01-01
In this Letter I point out that Hawking radiation is a purely kinematic effect that is generic to Lorentzian geometries. Hawking radiation arises for any test field on any Lorentzian geometry containing an event horizon regardless of whether or not the Lorentzian geometry satisfies the dynamical Einstein equations of general relativity. On the other hand, the classical laws of black hole mechanics are intrinsically linked to the Einstein equations of general relativity (or their perturbative extension into either semiclassical quantum gravity or string-inspired scenarios). In particular, the laws of black hole thermodynamics, and the identification of the entropy of a black hole with its area, are inextricably linked with the dynamical equations satisfied by the Lorentzian geometry: entropy is proportional to area (plus corrections) if and only if the dynamical equations are the Einstein equations (plus corrections). It is quite possible to have Hawking radiation occur in physical situations in which the laws...
Entropy and temperatures of Nariai black hole
Eune, Myungseok
2013-01-01
The statistical entropy of the Nariai black hole in a thermal equilibrium is calculated by using the brick wall method based on two different temperatures. The first form of the entropy is given by the unexpected form of the area for the Bousso-Hawking temperature, while the second form can be written by the ordinary area law for the Hawking temperature with the standard normalization. It turns out that the Wald entropy supports the case of the standard normalization of the Hawking temperature. We discuss some physical consequences of this result and the properties of the temperatures.
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...
Symmetries, Horizons, and Black Hole Entropy
Carlip, S
2007-01-01
Black holes behave as thermodynamic systems, and a central task of any quantum theory of gravity is to explain these thermal properties. A statistical mechanical description of black hole entropy once seemed remote, but today we suffer an embarrassment of riches: despite counting very different states, many inequivalent approaches to quantum gravity obtain identical results. Such ``universality'' may reflect an underlying two-dimensional conformal symmetry near the horizon, which can be powerful enough to control the thermal characteristics independent of other details of the theory. This picture suggests an elegant description of the relevant degrees of freedom as Goldstone-boson-like excitations arising from symmetry breaking by the conformal anomaly.
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)
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.
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.
Effective Conformal Descriptions of Black Hole Entropy
Directory of Open Access Journals (Sweden)
Steven Carlip
2011-07-01
Full Text Available It is no longer considered surprising that black holes have temperatures and entropies. What remains surprising, though, is the universality of these thermodynamic properties: their exceptionally simple and general form, and the fact that they can be derived from many very different descriptions of the underlying microscopic degrees of freedom. I review the proposal that this universality arises from an approximate conformal symmetry, which permits an effective “conformal dual” description that is largely independent of the microscopic details.
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.
Siegel Modular Forms and Black Hole Entropy
Belin, Alexandre; Gomes, Joao; Keller, Christoph A
2016-01-01
We discuss the application of Siegel Modular Forms to Black Hole entropy counting. The role of the Igusa cusp form $\\chi_{10}$ in the D1D5P system is well-known, and its transformation properties are what allows precision microstate counting in this case. We implement this counting for other Siegel modular and paramodular forms, and we show that they could serve as candidates for other types of black holes. We investigate the growth of their coefficients, identifying the dominant contributions and the leading logarithmic corrections in various regimes. We also discuss similarities and differences to the behavior of $\\chi_{10}$, and possible physical interpretations of such forms both from a microscopic and gravitational point of view.
Gravitational correlation, black hole entropy, and information conservation
He, DongShan; Cai, QingYu
2017-04-01
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 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.
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_...
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.
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.
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.
BTZ black hole entropy: a spin foam model description
Energy Technology Data Exchange (ETDEWEB)
Garcia-Islas, J Manuel [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, UNAM, A Postal 20-726, 01000, Mexico DF (Mexico)], E-mail: jmgislas@leibniz.iimas.unam.mx
2008-12-21
We present a microscopical explanation of the entropy of the BTZ black hole using discrete spin foam models of quantum gravity. The entropy of a black hole is given in geometrical terms which led us to think that its statistical description must be given in terms of a quantum geometry. In this paper we present it in terms of spin foam geometrical observables at the horizon of the black hole.
Black hole entropy thermodynamics, statistical-mechanics and subtraction procedure
Frolov, V P; Zelnikov, A I
1996-01-01
The thermodynamical one-loop entropy S^{TD} of a two-dimensional black hole in thermal equilibrium with the massless quantum gas is calculated. It is shown that S^{TD} includes the Bekenstein-Hawking entropy, evaluated for the quantum corrected geometry, and the finite difference of statistical mechanical entropies -Tr\\hat{\\rho}\\ln\\hat{\\rho} for the gas on the black hole and Rindler spaces. This result demonstrates in an explicit form that the relation between thermodynamical and statistical-mechanical entropies of a black hole is non-trivial and requires special subtraction procedure.
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
Directory of Open Access Journals (Sweden)
Wei Xu
2015-06-01
Full Text Available 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.
Entropy bound of horizons for charged and rotating black holes
Energy Technology Data Exchange (ETDEWEB)
Xu, Wei, E-mail: xuweifuture@gmail.com [School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China); Wang, Jia, E-mail: wangjia2010@mail.nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China); Meng, Xin-he, E-mail: xhm@nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China); State Key Laboratory of Institute of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China)
2015-06-30
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.
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.
Black hole entropy off-shell vs on-shell
Frolov, V P; Zelnikov, A I
1996-01-01
Different methods of calculation of quantum corrections to the thermodynamical characteristics of a black hole are discussed and compared. The relation between on-shell and off-shell approaches is established. The off-shell methods are used to explicitly demonstrate that the thermodynamical entropy S^{TD} of a black hole, defined by the first thermodynamical law, differs from the statistical-mechanical entropy S^{SM}, determined as S^{SM}=-\\mbox{Tr}(\\hat{\\rho}^H\\ln\\hat{\\rho}^H) for the density matrix \\hat{\\rho}^H of a black hole. It is shown that the observable thermodynamical black hole entropy can be presented in the form S^{TD}=\\pi {\\bar r}_+^2+S^{SM}-S^{SM}_{Rindler}. Here {\\bar r}_+ is the radius of the horizon shifted because of the quantum backreaction effect, and S^{SM}_{Rindler} is the statistical-mechanical entropy calculated in the Rindler space.
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 from conformal symmetry on the horizon
Carlip, Steven
2017-01-01
The idea that black hole entropy might be governed by a conformal symmetry is an old one, but until now most efforts have focused on either asymptotic symmetries or symmetries on a ``stretched horizon. For two-dimensional dilaton gravity, I show the existence of a well-behaved conformal symmetry that is on the horizon, with a central charge that correctly determines the black hole entropy. Supported by Department of Energy grant DE-FG02-91ER40674.
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...
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}
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.
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.
Spherically symmetric black-hole entropy without brick walls
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2003-11-01
Properties of the thermal radiation of black holes are discussed using a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst at the last stage of emission from a spherically symmetric black hole. When the new equation of state density is used to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static spherically symmetric 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 from 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.
Configurational entropy of anti-de Sitter black holes
Braga, Nelson R. F.; da Rocha, Roldão
2017-04-01
Recent studies indicate that the configurational entropy is an useful tool to investigate the stability and (or) the relative dominance of states for diverse physical systems. Recent examples comprise the connection between the variation of this quantity and the relative fraction of light mesons and glueballs observed in hadronic processes. Here we develop a technique for defining a configurational entropy for an AdS-Schwarzschild black hole. The achieved result corroborates consistency with the Hawking-Page phase transition. Namely, the dominance of the black hole configurational entropy will be shown to increase with the temperature. In order to verify the consistency of the new procedure developed here, we also consider the case of black holes in flat space-time. For such a black hole, it is known that evaporation leads to instability. The configurational entropy obtained for the flat space case is thoroughly consistent with the physical expectation. In fact, we show that the smaller the black holes, the more unstable they are. So, the configurational entropy furnishes a reliable measure for stability of black holes.
Absence of log correction in entropy of large black holes
Ghosh, A
2014-01-01
Earlier calculations of black hole entropy in loop quantum gravity have led to a dominant term proportional to the area, but there was a correction involving the logarithm of the area. We find however that calculations yield an entropy proportional to the area eigenvalue with no such correction if the area eigenvalue is taken to be much larger than the classical area.
Entropy product of rotating black holes in three-dimensions
Mahdavian Yekta, Davood
2017-03-01
It has been shown that the product of the entropies of the inner Cauchy and outer event horizon of the charged axisymmetric and stationary black holes is a universal formula, which is independent of the black hole's mass. In this paper, we investigate this universality for the two kinds of rotating black holes in the three-dimensional gravity models. In fact, we study the spacelike warped anti-de Sitter black hole in the new massive gravity and the Bañados, Teitelboim, and Zanelli black hole in the minimal massive gravity. We show that this rule is held in the first theory. By contrast, in the latter case which includes a holographic gravitational anomalous term, we obtain that the universality does not work and the product depends on the mass. As a complement to the above verification, we also study the thermodynamic properties of these black holes.
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.
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.
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 and the Problem of Universality
Carlip, S
2008-01-01
To derive black hole thermodynamics in any quantum theory of gravity, one must introduce constraints that ensure that a black hole is actually present. For a large class of black holes, the imposition of such ``horizon constraints'' allows the use of conformal field theory methods to compute the density of states, reproducing the correct Bekenstein-Hawking entropy in a nearly model-independent manner. This approach may explain the ``universality'' of black hole entropy, the fact that many inequivalent descriptions of quantum states all seem to give the same thermodynamic predictions. It also suggests an elegant picture of the relevant degrees of freedom, as Goldstone-boson-like excitations arising from symmetry breaking by a conformal anomaly induced by the horizon constraints.
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.
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 nice and simplifying `laboratory' for questions about the full theory.
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.
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 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.
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.
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.
Uncertainty relation and black hole entropy of Kerr spacetime
Institute of Scientific and Technical Information of China (English)
Hu Shuang-Qi; Zhao Ren
2005-01-01
The properties of thermal radiation are discussed by using a new equation of state density, which is motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of Kerr black hole. When the new equation of state density is utilized to investigate the entropy of a Bosonic field and Fermionic field outside the horizon of a static Kerr black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
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.
Uncertainty relation and black hole entropy of Kerr spacetime
Hu, Shuang-Qi; Zhao, Ren
2005-07-01
The properties of thermal radiation are discussed by using a new equation of state density, which is motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of Kerr black hole. When the new equation of state density is utilized to investigate the entropy of a Bosonic field and Fermionic field outside the horizon of a static Kerr black hole, the divergence appearing in the brick wall model is removed, without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
Letter: Dilatonic Black Hole Entropy Without Brick Walls
Ren, Zhao; Sheng-Li, Zhang
2004-09-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of dilatonic black hole. When the new equation of state density is utilized to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static dilatonic black hole, the divergence appearing in the brick wall model is removed, without any cutoff. It is derived from the contribution of the vicinity of the horizon that the entropy is proportional to the horizon area.
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.
Anomalies, Chern-Simons Terms and Black Hole Entropy
Azeyanagi, Tatsuo; Ng, Gim Seng
2015-01-01
Recent derivations of Cardy-like formulae in higher dimensional field theories have opened up a way of computing, via AdS/CFT, universal contributions to black hole entropy from gravitational Chern-Simons terms. Based on the manifestly covariant formulation of the differential Noether charge for Chern-Simons terms proposed in arXiv:1407.6364, we compute the entropy and asymptotic charges for the rotating charged AdS black holes in higher dimensions at leading order of the fluid/gravity derivative expansion in the Einstein-Maxwell-Chern-Simons system. This gives a result that exactly matches the field theory predictions from Cardy-like formulae.
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.
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...
Quantization of black hole entropy from unstable circular null geodesics
Wei, Shao-Wen; Liu, Yu-Xiao; Fu, Chun-E.
2016-04-01
The quasinormal mode frequencies can be understood from the massless particles trapped at the unstable circular null geodesics and slowly leaking out to infinity. Based on this viewpoint, in this paper, we semiclassically construct the entropy spectrum of the static and stationary black holes from the null geodesics. The result shows that the spacing of the entropy spectrum only depends on the property of the black hole in the eikonal limit. Moreover, for a black hole far from the extremal case, the spacing is found to be smaller than 2πħ for any dimension, which is very different from the result of the previous work by using the usual quasinormal mode frequencies.
Simple regular black hole with logarithmic entropy correction
Morales-Durán, Nicolás; Vargas, Andrés F.; Hoyos-Restrepo, Paulina; Bargueño, Pedro
2016-10-01
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 realises 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 generalised uncertainty principle. This similitude has been confirmed by the existence of a remnant, which prevents complete evaporation, in agreement with the quadratic generalised uncertainty principle case.
Black Holes, Entropies, and Semiclassical Spacetime in Quantum Gravity
Nomura, Yasunori
2014-01-01
We present a coherent picture of the quantum mechanics of black holes. The picture does not require the introduction of any drastically new physical effect beyond what is already known; it arises mostly from synthesizing and (re)interpreting existing results in appropriate manners. We identify the Bekenstein-Hawking entropy as the entropy associated with coarse-graining performed to obtain semiclassical field theory from a fundamental microscopic theory of quantum gravity. This clarifies the issues around the unitary evolution, the existence of the interior spacetime, and the thermodynamic nature in black hole physics--any result in semiclassical field theory is a statement about the maximally mixed ensemble of microscopic quantum states consistent with the specified background, within the precision allowed by quantum mechanics. We present a detailed analysis of information transfer in Hawking emission and black hole mining processes, clarifying what aspects of the underlying dynamics are (not) visible in sem...
Simple regular black hole with logarithmic entropy correction
Energy Technology Data Exchange (ETDEWEB)
Morales-Duran, Nicolas; Vargas, Andres F.; Hoyos-Restrepo, Paulina; Bargueno, Pedro [Universidad de los Andes, Departamento de Fisica, Bogota, Distrito Capital (Colombia)
2016-10-15
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 realises 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 generalised uncertainty principle. This similitude has been confirmed by the existence of a remnant, which prevents complete evaporation, in agreement with the quadratic generalised uncertainty principle case. (orig.)
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.
Black holes, entropies, and semiclassical spacetime in quantum gravity
Nomura, Yasunori; Weinberg, Sean J.
2014-10-01
We present a coherent picture of the quantum mechanics of black holes. The picture does not require the introduction of any drastically new physical effect beyond what is already known; it arises mostly from synthesizing and (re)interpreting existing results in appropriate manners. We identify the Bekenstein-Hawking entropy as the entropy associated with coarse-graining performed to obtain semiclassical field theory from a fundamental microscopic theory of quantum gravity. This clarifies the issues around the unitary evolution, the existence of the interior spacetime, and the thermodynamic nature in black hole physics — any result in semiclassical field theory is a statement about the maximally mixed ensemble of microscopic quantum states consistent with the specified background, within the precision allowed by quantum mechanics. We present a detailed analysis of information transfer in Hawking emission and black hole mining processes, clarifying what aspects of the underlying dynamics are (not) visible in semiclassical field theory. We also discuss relations between the black hole entropy and the entanglement entropy across the horizon. We then extend our discussions to more general contexts in quantum gravity. The subjects include extensions to de Sitter and Minkowski spaces and implications for complementarity and cosmology, especially the eternally inflating multiverse.
Toward a spin foam model description of black hole entropy
Energy Technology Data Exchange (ETDEWEB)
Garcia-Islas, J Manuel [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, UNAM, A Postal 20-726, 01000, Mexico DF (Mexico)], E-mail: jmgislas@leibniz.iimas.unam.mx
2008-12-07
We propose a way to describe the origin of black hole entropy in the spin foam models of quantum gravity. This stimulates a new way to study the relation of spin foam models and loop quantum gravity. (comments, replies and notes)
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.
Dirty black holes Entropy as a surface term
Visser, M
1993-01-01
It is by now clear that the naive rule for the entropy of a black hole, {entropy} = 1/4 {area of event horizon}, is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This note performs two functions. Firstly, a rather different proof of this result is presented --- a proof based on Euclidean signature techniques. The total entropy is S = 1/4 {k A_H / l_P^2} + \\int_H {S} \\sqrt{g} d^2x. The integration runs over a spacelike cross-section of the event horizon H. The surface entropy density, {S}, is related to the behaviour of the matter Lagrangian under time dilations. Secondly, I shall consider the specific case of Einstein-Hilbert gravity coupled to an effective Lagrangian that is an arbitrary function of the Riemann ten...
Black hole entropy divergence and the uncertainty principle
Brustein, Ram
2011-01-01
Black hole entropy has been shown by 't Hooft to diverge at the horizon. The region near the horizon is in a thermal state, so entropy is linear to energy which consequently also diverges. We find a similar divergence for the energy of the reduced density matrix of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. This divergence is due to an infinitely sharp boundary, and it stems from the position/momentum uncertainty relation in the same way that the momentum fluctuations of a precisely localized quantum particle diverge. We show that when the boundary is smoothed the divergence is tamed. We argue that the divergence of black hole entropy can also be interpreted as a consequence of position/momentum uncertainty, and that 't Hooft's brick wall tames the divergence in the same way, by smoothing the boundary.
On the Microcanonical Entropy of a Black Hole
Bhaduri, R K; Das, S; Bhaduri, Rajat K.; Tran, Muoi N.; Das, Saurya
2003-01-01
It has been suggested recently that the microcanonical entropy of a system may be accurately reproduced by including a logarithmic correction to the canonical entropy. In this paper we test this claim both analytically and numerically by considering three simple thermodynamic models whose energy spectrum may be defined in terms of one quantum number only, as in a non-rotating black hole. The first two pertain to collections of noninteracting bosons, with logarithmic and power-law spectra. The last is an area ensemble for a black hole with equi-spaced area spectrum. In this case, the many-body degeneracy factor can be obtained analytically in a closed form. We also show that in this model, the leading term in the entropy is proportional to the horizon area A, and the next term is ln A with a negative coefficient.
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.
Entanglement Entropy of Two Black Holes and Entanglement Entropic Force
Shiba, Noburo
2010-01-01
We study the entanglement entropy, $S_C$, of a massless free scalar field on the outside region $C$ of two black holes $A$ and $B$ whose radii are $R_1$ and $R_2$ and how it depends on the distance, $r(\\gg R_1,R_2)$, between two black holes. If we can consider the entanglement entropy as thermodynamic entropy, we can see the entropic force acting on the two black holes from the $r$ dependence of $S_C$. We develop the computational method based on that of Bombelli et al to obtain the $r$ dependence of $S_C$ of scalar fields whose Lagrangian is quadratic with respect to the scalar fields. First we study $S_C$ in $d+1$ dimensional Minkowski spacetime. In this case the state of the massless free scalar field is the Minkowski vacuum state and we replace two black holes by two imaginary spheres, and we take the trace over the degrees of freedom residing in the imaginary spheres. We obtain the leading term of $S_C$ with respect to $1/r$. The result is $S_C=S_A+S_B+\\tfrac{1}{r^{2d-2}} G(R_1,R_2)$, where $S_A$ and $S_...
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...
Martínez-Merino, Aldo; Ryan, Michael P
2016-01-01
Newtonian gravitation with some slight modifications, along with some highly simplified ideas from quantum field theory allow us to reproduce, at least at the level of back-of-the-envelope calculations, many results of black hole physics. We consider particle production by a black hole, the Newtonian equivalent of the Hawking temperature, and the Bekenstein entropy. Also, we are able to deduce Newtonian field equations from entropy. We finally study higher-order Newtonian theories under the same assumptions used for ordinary Newtonian theory. In a companion article we will look at entropic forces for various entropies and make contact with our analysis of higher-order Newtonian theories.
Correlation, entropy, and information transfer in black hole radiation
Zhang, Baocheng; Zhan, Mingsheng; You, Li
2014-01-01
Since the discovery of Hawking radiation, its consistency with quantum theory has been widely questioned. In the widely described picture, irrespective of what initial state a black hole starts with before collapsing, it eventually evolves into a thermal state of Hawking radiations after the black hole is exhausted. This scenario violates the principle of unitarity as required for quantum mechanics and leads to the acclaimed "information loss paradox". This paradox has become an obstacle or a reversed touchstone for any possible theory to unify the gravity and quantum mechanics. Based on the results from Hawking radiation as tunneling, we recently show that Hawking radiations can carry off all information about the collapsed matter in a black hole. After discovering the existence of information-carrying correlation, we show in great detail that entropy is conserved for Hawking radiation based on standard probability theory and statistics. We claim that information previously considered lost remains hidden ins...
Thermodynamics of Coherent States and Black Hole Entropy
Bashkirov, A G
2001-01-01
Mean values of any observable variable are always calculated in a coherent state as in a mixed state because the coherent state is an eigenstate of non-Hermitian operator. Thus, we propose the concept of a coherent ensemble closely resemble the canonical ensemble. The entropy and temperature are naturally defined for the coherent ensemble. As an example, entropy and temperature are evaluated for coherent states of a harmonic oscillator and quantum field described by the Klein-Gordon-Fock equation with a source term. It is shown, in particular, that the temperature of the coherent oscillator coincides with the effective temperature of a harmonic oscillator being in contact with a heath bath (Bloch formula) when the bath temperature tends to zero. The Bekenstein-Hawking entropy and temperature of a black hole can also be interpreted as an entropy and temperature of coherent states of a physical vacuum in the vicinity of a horizon surface.
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.
Black hole entropy and Lorentz-diffeomorphism Noether charge
Jacobson, Ted; Mohd, Arif
2015-01-01
We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvat...
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.)
Functional determinants, index theorems, and exact quantum black hole entropy
Murthy, Sameer; Reys, Valentin
2015-12-01
The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.
Functional determinants, index theorems, and exact quantum black hole entropy
Murthy, Sameer
2015-01-01
The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the $Q\\mathcal{V}$ operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around $Q$-invariant off-shell configurations in four-dimensional $\\mathcal{N}=2$ supergravity with $AdS_{2} \\times S^{2}$ boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in $\\mathcal{N}=2$ supergravity. We explain cancellations concerning $\\frac18$-BPS black holes in $\\mathcal{N}=8$ supergravity that were observed previously. We also make comments about the interpretation of...
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.
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.
Entropy spectrum of charged BTZ black holes in massive gravity's rainbow
Panah, Behzad Eslam
2016-01-01
Regarding the significant interests in massive gravity's rainbow and also BTZ black holes, we apply the formalism introduced by Jiang and Han in order to investigate the quantization of the entropy of black holes. We show that the entropy of BTZ black holes in massive gravity's rainbow is quantized with equally spaced spectra and it depends on the value of the parameters of this black hole such as; massive parameters, electrical charge, the cosmological constant and also rainbow functions.
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.
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...
Generalized Mirror Symmetry and Quantum Black Hole Entropy
Ferrara, Sergio
2012-01-01
We find general relations between the on-shell gravitational trace anomaly A_N, and the logarithmic correction Delta S_N to the entropy of "large" BPS extremal black holes in N>1 supergravity theories in D=4 space-time dimensions (recently computed by Sen [arXiv:1108.3842]). For (generalized) self-mirror theories (all having A_N = 0), we obtain the result DeltaS_N = - Delta S_(8-N) = 2 - N/2, whereas for generic theories the trace anomaly tildeA_N of the fully dualized theory turns out to coincide with 2Delta S_N, up to a model-independent shift: tildeA_N = 2Delta S_N - 1. We also speculate on N=1 theories displaying "large" extremal black hole solutions.
Holographic entropy of Warped-AdS$_3$ black holes
Donnay, Laura
2015-01-01
We study the asymptotic symmetries of three-dimensional Warped Anti-de Sitter (WAdS) spaces in three-dimensional New Massive Gravity (NMG). For a specific choice of asymptotic boundary conditions, we find that the algebra of charges is infinite-dimensional and coincides with the semidirect sum of Virasoro algebra with non-vanishing central charge and an affine $\\hat{u}(1)_k$ Ka\\v{c}-Moody algebra. We show that the WAdS black hole configurations organize in terms of two commuting Virasoro algebras. We identify the Virasoro generators that expand the associated representations in the dual Warped Conformal Field Theory (WCFT) and, by applying the Warped version of the Cardy formula, we prove that the microscopic WCFT computation exactly reproduces the entropy of black holes in WAdS space.
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 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.
Black hole entropy and Lorentz-diffeomorphism Noether charge
Jacobson, Ted
2015-01-01
We show that, in the first or second order orthonormal frame formalism, black hole entropy is the horizon Noether charge for a combination of diffeomorphism and local Lorentz symmetry involving the Lie derivative of the frame. The Noether charge for diffeomorphisms alone is unsuitable, since a regular frame cannot be invariant under the flow of the Killing field at the bifurcation surface. We apply this formalism to Lagrangians polynomial in wedge products of the frame field 1-form and curvature 2-form, including general relativity, Lovelock gravity, and "topological" terms in four dimensions.
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.
Quantum Liouville theory and BTZ black hole entropy
Chen, Y
2004-01-01
In this paper I give an explicit conformal field theory description of (2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field theory I investigate the reducible Verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra U_q(sl_2) \\odot U_{\\hat{q}}(sl_2). I show that there are states that decouple from these reducible Verma modules in a similar fashion to the decoupling of null states in minimal models. Because ofthe nonstandard form of the Ward identity for the two-point correlation functions in quantum Liouville field theory, these decoupling states have positive-definite norms. The explicit counting from these states gives the desired Bekenstein-Hawking entropy in the semi-classical limit when q is a root of unity of odd order.
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.
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.
Angular Momentum-Free of the Entropy Relations for Rotating Kaluza-Klein Black Holes
Liu, Hang; Meng, Xin-he
2017-02-01
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≥4, 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≥5, 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 δ=0. For the reason that the entropy relations of charged rotating Kaluza-Klein black holes as well as the non-charged rotating Kaluza-Klein black holes in asymptotically flat spacetime act the same way, it is found that the charge has no effect in the angular momentum-independence of entropy sum and product in asymptotically flat spactime.
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
Energy Technology Data Exchange (ETDEWEB)
Anacleto, M.A., E-mail: anaclet@df.ufcg.edu.br [Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraíba (Brazil); Brito, F.A., E-mail: fabrito@df.ufcg.edu.br [Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraíba (Brazil); Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970 João Pessoa, Paraíba (Brazil); Passos, E., E-mail: passos@df.ufcg.edu.br [Departamento de Física, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraíba (Brazil)
2015-10-07
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.
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.
Gravitational collapse and entropy of Black Holes with magnetic sources
Rey, A Ulacia
2011-01-01
This thesis is divided in two parts, each one addressing problems that can be relevant in the study of compact objects. The first part deals with the study of a magnetized and self-gravitating gas of degenerated fermions (electrons and neutrons) as sources of a Bianchi-I space-time. We solve numerically the Einstein-Maxwell field equations for a large set of initial conditions of the dynamical variables. The collapsing singularity is isotropic for the neutron gas and can be anisotropic for the electron gas. This result is consistent with the fact that electrons exhibit a stronger coupling with the magnetic field, which is the source of anisotropy in the dynamical variables. In the second part we calculate the entropy of extremal black holes in 4 and 5 dimensions, using the entropy function formalism of Sen and taking into account higher order derivative terms that come from the complete set of Riemann invariants. The resulting entropies show the deviations from the well know Bekenstein-Hawking area law.
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 from Indistinguishable Quantum Geometric Excitations
Directory of Open Access Journals (Sweden)
Abhishek Majhi
2016-01-01
Full Text Available In loop quantum gravity the quantum geometry of a black hole horizon consists of discrete nonperturbative quantum geometric excitations (or punctures labeled by spins, which are responsible for the quantum area of the horizon. If these punctures are compared to a gas of particles, then the spins associated with the punctures can be viewed as single puncture area levels analogous to single particle energy levels. Consequently, if we assume these punctures to be indistinguishable, the microstate count for the horizon resembles that of Bose-Einstein counting formula for gas of particles. For the Bekenstein-Hawking area law to follow from the entropy calculation in the large area limit, the Barbero-Immirzi parameter (γ approximately takes a constant value. As a by-product, we are able to speculate the state counting formula for the SU(2 quantum Chern-Simons theory coupled to indistinguishable sources in the weak coupling limit.
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...
Nernst Theorem and Statistical Entropy of 5-Dimensional Rotating Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAORen; WUYue-Qin; ZHANGLi-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 and topology of the Kerr-de Sitter black hole
Institute of Scientific and Technical Information of China (English)
陈松柏; 荆继良
2002-01-01
By using the path integral method of Gibbons and Hawking, the entropy of the Kerr-de Sitter black hole isinvestigated under the microcanonical ensemble. We find that the entropy is one eighth the sum of the products of theEuler number of its cosmological horizon and event horizon with their respective areas. It is shown that the origin ofthe entropy of the black hole is related to the topology of its instanton.
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...
Superradiance and statistical entropy of hairy black hole in three dimensions
Eune, Myungseok; Kim, Wontae
2013-01-01
We calculate the statistical entropy of a rotating hairy black hole by taking into account superradiant modes in the brick wall method. The UV cutoff is independent of the scalar hair, which gives the well-defined area law of the entropy. It can be shown that the angular momentum and the energy of matter field depend on the scalar hair. For the vanishing scalar hair, it turns out that the energy for matter is related to both the black hole mass and the black hole angular momentum whereas the angular momentum for matter field is directly proportional to the angular momentum of the black hole.
Superradiance and statistical entropy of a hairy black hole in three dimensions
Eune, Myungseok; Gim, Yongwan; Kim, Wontae
2013-08-01
We calculate the statistical entropy of a rotating hairy black hole by taking into account superradiant modes in the brick wall method. The UV cutoff is independent of the gravitational hair, which gives the well-defined area law of the entropy. It can be shown that the angular momentum and the energy of matter field depend on the gravitational hair. For the vanishing gravitational hair, it turns out that the energy for matter is related to both the black hole mass and the black hole angular momentum whereas the angular momentum for matter field is directly proportional to the angular momentum of the black hole.
From bricks to quasinormal modes: A new perspective on black hole entropy
Arzano, Michele; Dreyer, Olaf
2013-01-01
Calculations of black hole entropy based on the counting of modes of a quantum field propagating in a Schwarzschild background need to be regularized in the vicinity of the horizon. To obtain the Bekenstein-Hawking result the short distance cut-off needs to be fixed by hand. In this note we give an argument for obtaining this cut-off in a natural fashion. We do this by modelling the black hole by its set of quasinormal modes. The horizon then becomes a extended region: the quantum ergosphere. The interaction of the quantum ergosphere and the quantum field provides a natural regularization mechanism. The width of the quantum ergosphere provides the right cut-off for the entropy calculation. We arrive at a dual picture of black hole entropy. The entropy of the black hole is given both by the entropy of the quantum field in the bulk and the dynamical degrees of freedom on the horizon.
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.
The Entropy of the BTZ Black Hole and AdS/CFT Correspondence
Lee, T
1998-01-01
We construct an action, which governs the dynamics of the Bañados-Teitelboim-Zanelli (BTZ) black hole and perform the canonical quantization. The quantum action is given by a $SL(2,R)$ Wess-Zumino-Witten model on the boundary coupled to the classical anti-de Sitter background, representing a massless BTZ black hole. The coupling, determined by a one-cocyle condition, is found to give dominant contribution to the central charge of Virasoro algebra. The entropy of the BTZ black hole is discussed from the point view of the AdS/CFT correspondence and an explanation is given to the puzzle of black hole entropy in the BTZ case. The BTZ black hole is a quantum object and the BTZ black hole with finite mass should be considered as a quantum excitation of the massless one.
Entanglement entropy of charged dilaton-axion black hole and quantum isolated horizon
Yang, Ze-Min; Li, Xiu-Lan; Gao, Ying
2016-09-01
Based on the work of Ghosh and Perez, we calculate the statistical entropy of charged dilaton-axion black hole. In the calculations we take the integral from the position of QIH to infinity, so the obtained entropy is the entanglement entropy outside the QIH. It is shown that only if the position of QIH is properly chosen the leading term of logarithm of the number of quantum states on the QIH is equal to the leading term of the entanglement entropy outside the black hole horizon, and both are the Bekenstein-Hawking entropy. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states.
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.
First quantum correction to entropy of Vaidya-Bonner black holes due to arbitrary spin fields
Institute of Scientific and Technical Information of China (English)
高长军; 沈有根
2002-01-01
Using the improved brick-wall model, we have calculated the first quantum correction to the entropy of non-staticblack holes, Vaidya-Bonner black holes, due to the gravitational, electro-magnetic and neutrino fields. The result showsthat both bosonic entropy and fermionic entropy are exactly proportional to the area of the event horizon. Thus, theentropy-area law still holds in such a non-static case.
An improved estimate of black hole entropy in the quantum geometry approach
Ghosh, A
2005-01-01
The corrected counting of states for black holes in the quantum geometry approach shows that the dominant configurations are distributions of spins that include spins exceeding one-half at the punctures. This alters the value of the Immirzi parameter and the black hole entropy. The logarithmic correction coefficient is -1/2 as before.
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.
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.
Quantum Correction to Entropy of the Kerr Black Hole due to Rarita-Schwinger Fields
Institute of Scientific and Technical Information of China (English)
荆继良
2003-01-01
Quantum correction to entropy of the Kerr black hole arising from Rarita-Schwinger fields is studied by using the Newman-Penrose formalism and brick-wall model. It is shown that contribution of spin to the logarithmic term of the quantum correction is dependent on both the square of spin of the particle and the rotation of the black hole. For different values of a/r+, the subleading term can increase or decrease, or cannot affect the entropy.
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.
An Elementary Derivation of The Black Hole Entropy in Any Dimension
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Carlos Castro
2001-03-01
Full Text Available Abstract: An elementary derivation of the Black Hole Entropy area relation in any dimension is provided based on the New Extended Scale Relativity Principle and Shannon's Information Entropy. The well known entropy-area linear Bekenstein-Hawking relation is derived. We discuss briefly how to derive the most recently obtained Logarithmic and higher order corrections to the linear entropy-area law in full agreement with the standard results in the literature.
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.
Directory of Open Access Journals (Sweden)
Hang Liu
2016-08-01
Full Text Available 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.
Intersecting D-branes and black hole entropy
Behrndt, Klaus; Bergshoeff, Eric
1996-01-01
In four dimensions there are 4 different types of extremal Maxwell/scalar black holes characterized by a scalar coupling parameter a with a = 0, 1/âˆš3, 1, âˆš3. These black holes can be described as intersections of ten-dimensional non-singular Ramond-Ramond objects, i.e, D-branes, waves and Taub-N
Entropy of Reissner-Nordstrom-De Sitter Black Hole in Nonthermal Equilibrium
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; ZHANG Jun-Fang; ZHANG Li-Chun
2002-01-01
By making use of the method of quantum statistics, we directly derive the partition function of bosonic and fermionic fields in Reissner-Nordstrom-De Sitter black hole and obtain the integral expression of black hole's entropy and the entropy to which the cosmic horizon surface corresponds. It avoids the difficulty in solving the wave equation of various particles. Then via the improved brick-wall method, i.e. the membrane model, we calculate black hole's entropy and cosmic entropy and find out that if we let the integral upper limit and lower limit both tend to the horizon, the entropy of black hole is proportional to the area of horizon and the entropy to which cosmic horizon surface corresponds is proportional to the area of cosmic horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. In the whole process, the physical idea is clear and the calculation is simple.We offer a new simple and direct way for calculating the entropy of different complicated black holes.
Entropy of an extremal electrically charged thin shell and the extremal black hole
Lemos, José P S; Zaslavskii, Oleg B
2015-01-01
There is a debate as to what is the value of the the entropy $S$ of extremal black holes. There are approaches that yield zero entropy $S=0$, while there are others that yield the Bekenstein-Hawking entropy $S=A_+/4$, in Planck units. There are still other approaches that give that $S$ is proportional to $r_+$ or even that $S$ is a generic well-behaved function of $r_+$. Here $r_+$ is the black hole horizon radius and $A_+=4\\pi r_+^2$ is its horizon area. Using a thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is $S=S(r_+)$, i.e., the entropy of an extremal black hole is a function of $r_+$ alone. We speculate that the range of values for the entropy of an extremal black hole is $0\\leq S(r_+) \\leq A_+/4$.
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.
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 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.
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.)
Black hole entropy with and without log correction in loop quantum gravity
Mitra, P
2014-01-01
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.
Entropy of an extremal electrically charged thin shell and the extremal black hole
Directory of Open Access Journals (Sweden)
José P.S. Lemos
2015-11-01
Full Text Available There is a debate as to what is the value of the entropy S of extremal black holes. There are approaches that yield zero entropy S=0, while there are others that yield the Bekenstein–Hawking entropy S=A+/4, in Planck units. There are still other approaches that give that S is proportional to r+ or even that S is a generic well-behaved function of r+. Here r+ is the black hole horizon radius and A+=4πr+2 is its horizon area. Using a spherically symmetric thin matter shell with extremal electric charge, we find the entropy expression for the extremal thin shell spacetime. When the shell's radius approaches its own gravitational radius, and thus turns into an extremal black hole, we encounter that the entropy is S=S(r+, i.e., the entropy of an extremal black hole is a function of r+ alone. We speculate that the range of values for an extremal black hole is 0≤S(r+≤A+/4.
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.
A Proposed Absolute Entropy of Near Extremal Kerr-Newman Black Hole
Lin, H
2001-01-01
Some problems have been found as to the definition of entropy of black hole being applied to the extremal Kerr-Newman case, which has conflicts with the third law of thermodynamics. We have proposed a new modification for the near extremal one, which not only obeys the third law, but also does not conflict with other results in black hole thermodynamics. Then we proved that the inner horizon has temperature and proposed that the inner horizon contributes to the entropy of the near extremal one so that the entropy of it has a modified form and vanishes at absolute zero temperature.
Entropy of Reissner–Nordström–de Sitter black hole
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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.
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...
The entropy of an acoustic black hole in Bose-Einstein condensates
Rinaldi, Massimiliano
2011-01-01
We compute the entropy associated to the Hawking emission of a $(1+1)$-dimensional acoustic black hole in a Bose-Einstein condensate. We use the brick wall model proposed by 't Hooft, adapted to the momentum space, in order to tackle the case when high frequency dispersion is taken in account. As expected, we find that in the hydrodynamic limit the entropy only depends on the size of the box in the near-horizon region, as for gravitational $(1+1)$-dimensional black holes. When dispersion effects are considered, we find an additional contribution that depends on the size of the near-horizon region measured in units of healing length. Moreover, the size of the box is fixed by the black hole parameters, and the leading term contribution to the entropy can be uniquely determined. We find that the leading term entropy is constant and much larger than the corrections.
Energy Technology Data Exchange (ETDEWEB)
Yan, Hao-Peng; Liu, Wen-Biao, E-mail: wbliu@bnu.edu.cn
2016-08-10
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.
Directory of Open Access Journals (Sweden)
Hao-Peng Yan
2016-08-01
Full Text Available 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.
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...
Entropy/Area spectra of the charged black hole from quasinormal modes
Wei, Shao-Wen; Yang, Ke; Zhong, Yuan
2010-01-01
With the new physical interpretation of quasinormal modes proposed by Maggiore, the quantum area spectra of black holes have been investigated recently. It is shown that, the area spectrum for a non-rotating black hole with no charge is equidistant. While, for a rotating black hole, it is non-equidistant and depends on the angle momentum $J$. So, it is worth to investigate the area spectrum for a charged black hole. Following the Kunstatter's method, we obtain the area spectrum and entropy spectrum of the charged Garfinkle-Horowitz-Strominger black hole, originated from the effective action that emerges in the low-energy of string theory. Both the area spectrum and entropy spectrum are found to be equally spaced and do not depend on the charge $q$, which is different from that of the rotating black hole. Combing with possible observational data from gravity waves, we hope our results can give us answers to the open questions such as the 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.
Directory of Open Access Journals (Sweden)
Songbai Chen
2015-12-01
Full Text Available We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein–Hawking term in the black hole entropy. The corrected classical Bekenstein–Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein–Hawking entropy depends not only on the black hole parameter, but also on the coupling which reduces Lorentz violation.
Energy Technology Data Exchange (ETDEWEB)
Chen, Songbai, E-mail: csb3752@hunnu.edu.cn [Institute of Physics and Department of Physics, Hunan Normal University, Changsha, Hunan 410081 (China); Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081 (China); Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Jing, Jiliang, E-mail: jljing@hunnu.edu.cn [Institute of Physics and Department of Physics, Hunan Normal University, Changsha, Hunan 410081 (China); Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081 (China); Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Liao, Hao [Institute of Physics and Department of Physics, Hunan Normal University, Changsha, Hunan 410081 (China); Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, Hunan 410081 (China); Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, Hunan 410081 (China); State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China)
2015-12-17
We have investigated quantum entropy of a static black hole arising from the massless scalar field with Lorentz violation induced by the coupling to Einstein tensor. Our results show that the coupled massless scalar field contributes to the classical Bekenstein–Hawking term in the black hole entropy. The corrected classical Bekenstein–Hawking entropy is not one quarter of the event horizon area of the original background black hole, but of a corresponding effective metric related to the coupling. It means that the classical Bekenstein–Hawking entropy depends not only on the black hole parameter, but also on the coupling which reduces Lorentz violation.
Mechanism of Generation of Black Hole Entropy in Sakharov's Induced Gravity
Frolov, V P
1997-01-01
The mechanism of generation of the Bekenstein-Hawking entropy $S^{BH}$ of a black hole in the Sakharov's induced gravity is proposed. It is suggested that the "physical" degrees of freedom, which explain the entropy $S^{BH}$, form only a finite subset of the standard Rindler-like modes defined outside the black hole horizon. The entropy $S_R$ of the Rindler modes, or entanglement entropy, is always ultraviolet divergent, while the entropy of the "physical" modes is finite and it coincides in the induced gravity with $S^{BH}$. The two entropies $S^{BH}$ and $S_R$ differ by a surface integral Q interpreted as a Noether charge of non-minimally coupled scalar constituents of the model. We demonstrate that energy E and Hamiltonian H of the fields localized in a part of space-time, restricted by the Killing horizon $\\Sigma$, differ by the quantity $T_H Q$, where $T_H$ is the temperature of a black hole. The first law of the black hole thermodynamics enables one to relate the probability distribution of fluctuations...
Semiclassical corrections to black hole entropy and the generalized uncertainty principle
Energy Technology Data Exchange (ETDEWEB)
Bargueño, Pedro, E-mail: p.bargueno@uniandes.edu.co [Departamento de Física, Universidad de los Andes, Apartado Aéreo 4976, Bogotá, Distrito Capital (Colombia); Vagenas, Elias C., E-mail: elias.vagenas@ku.edu.kw [Theoretical Physics Group, Department of Physics, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)
2015-03-06
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.
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.
A Statistical Mechanical Interpretation of Black Hole Entropy Based on an Orthonormal Frame Action
Epp, R J
1998-01-01
Carlip has shown that the entropy of the three-dimensional black hole has its origin in the statistical mechanics of microscopic states living at the horizon. Beginning with a certain orthonormal frame action, and applying similar methods, I show that an analogous result extends to the (Euclidean) black hole in any spacetime dimension. However, this approach still faces many interesting challenges, both technical and conceptual.
Universal Corrections to Black Hole Entropy in $\\mathcal{N} \\geq 2$ Supergravity
Charles, Anthony M
2015-01-01
We embed general solutions to 4D Einstein-Maxwell theory into $\\mathcal{N} \\geq 2$ supergravity and study quadratic fluctuations of the supergravity fields around the background. We compute one-loop quantum corrections for all fields and show that the $c$-anomaly vanishes for complete $\\mathcal{N}=2$ multiplets. Logarithmic corrections to the entropy of Kerr-Newman black holes are therefore universal and independent of black hole parameters.
Thermodynamic Relations for the Entropy and Temperature of Multi-Horizon Black Holes
Directory of Open Access Journals (Sweden)
Wei Xu
2015-02-01
Full Text Available We present some entropy and temperature relations of multi-horizons, even including the “virtual” horizon. These relations are related to the product, division and sum of the entropy and temperature of multi-horizons. We obtain the additional thermodynamic relations of both static and rotating black holes in three- and four-dimensional (AdS spacetime. Especially, a new dimensionless, charge-independence and T+S+ = T_S_-like relation is presented. This relation does not depend on the mass, electric charge, angular momentum and cosmological constant, as it is always a constant. These relations lead us to obtaining some interesting thermodynamic bounds of entropy and temperature, including the Penrose inequality, which is the first geometrical inequality of black holes. Besides, based on these new relations, one can obtain the first law of thermodynamics and the Smarr relation for all horizons of a black hole.
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.
A Proposed Absolute Entropy of Near Extremal Kerr-Newman Black Hole
Lin, Hai
2001-01-01
Some problems have been found as to the definition of entropy of black hole being applied to the extremal Kerr-Newman case, which has conflicts with the third law of thermodynamics. We have proposed a new modification for the near extremal one, which not only obeys the third law, but also does not conflict with other results in black hole thermodynamics. Then we proved that the inner horizon has temperature and proposed that the inner horizon contributes to the entropy of the near extremal on...
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.
Reissner-Nordström black-hole entropy without brick walls
Ren, Zhao; Shuangqi, Hu
2004-02-01
The properties of the thermal radiation are discussed by using the new equation of state density motivated by the generalized uncertainty relation in the quantum gravity. There is no burst at the last stage of the emission of the Reissner-Nordström black hole. When the new equation of state density is utilized to investigate the entropy of a bosonic field and a fermionic field outside the horizon of a static Reissner-Nordström black hole, the divergence appearing in the brick wall model is removed, without any cut-off. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.
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.
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.
An equal area law for holographic entanglement entropy of the AdS-RN black hole
Nguyen, Phuc H.
2015-12-01
The Anti-de Sitter-Reissner-Nordström (AdS-RN) black hole in the canonical ensemble undergoes a phase transition similar to the liquid-gas phase transition, i.e. the isocharges on the entropy-temperature plane develop an unstable branch when the charge is smaller than a critical value. It was later discovered that the isocharges on the entanglement entropy -temperature plane also exhibit the same van der Waals-like structure, for spherical entangling regions. In this paper, we present numerical results which sharpen this similarity between entanglement entropy and black hole entropy, by showing that both of these entropies obey Maxwell's equal area law to an accuracy of around 1%. Moreover, we checked this for a wide range of size of the spherical entangling region, and the equal area law holds independently of the size. We also checked the equal area law for AdS-RN in 4 and 5 dimensions, so the conclusion is not specific to a particular dimension. Finally, we repeated the same procedure for a similar, van der Waals-like transition of the dyonic black hole in AdS in a mixed ensemble (fixed electric potential and fixed magnetic charge), and showed that the equal area law is not valid in this case. Thus the equal area law for entanglement entropy seems to be specific to the AdS-RN background.
Self-similarity, conservation of entropy/bits and the black hole information puzzle
Energy Technology Data Exchange (ETDEWEB)
Singleton, Douglas [Department of Physics, California State University Fresno,2345 East San Ramon Avenue M/S MH37, Fresno, CA 93740-8031 (United States); Department of Physics, Institut Teknologi Bandung,Jalan Ganesha 10, Bandung 40132 (Indonesia); Vagenas, Elias C. [Theoretical Physics Group, Department of Physics, Kuwait University,P.O. Box 5969, Safat 13060 (Kuwait); Zhu, Tao [GCAP-CASPER, Physics Department, Baylor University,One Bear Place, # 97316, Waco, TX 76798-7316 (United States); Institute for Advanced Physics & Mathematics, Zhejiang University of Technology,18 Chao-Wang Rd, Hangzhou, 310032 (China)
2014-05-19
John Wheeler coined the phrase “it from bit” or “bit from it” in the 1980s. However, much of the interest in the connection between information, i.e. “bits”, and physical objects, i.e. “its”, stems from the discovery that black holes have characteristics of thermodynamic systems having entropies and temperatures. This insight led to the information loss problem — what happens to the “bits” when the black hole has evaporated away due to the energy loss from Hawking radiation? In this essay we speculate on a radical answer to this question using the assumption of self-similarity of quantum correction to the gravitational action and the requirement that the quantum corrected entropy be well behaved in the limit when the black hole mass goes to zero.
Gupta, Rajesh Kumar; Jeon, Imtak
2015-01-01
We use the techniques of supersymmetric localization to compute the BPS black hole entropy in N=2 supergravity. We focus on the n_v+1 vector multiplets on the black hole near horizon background which is AdS_2 x S^2 space. We find the localizing saddle point of the vector multiplets by solving the localization equations, and compute the exact one loop partition function on the saddle point. Furthermore, we propose the appropriate functional integration measure. Through this measure, the one loop determinant is written in terms of the radius of the physical metric, which depends on the localizing saddle point value of the vector multiplets. The result for the one loop determinant is consistent with the logarithmic corrections to the BPS black hole entropy from vector multiplets.
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.
Quantum-corrected two-dimensional Horava-Lifshitz black hole entropy
Anacleto, M A; Brito, F A; Mota-Silva, J C
2015-01-01
In this paper we focus on the Halmiton-Jacobi method to determine the temperature and the entropy of a two-dimensional Horava-Lifshitz black hole by using the generalized uncertainty principles (GUP). We also address the product of horizons, mainly concerning the event, Cauchy, cosmological and virtual horizons.
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.
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 ...
Rényi entropy and the thermodynamic stability of black holes
Energy Technology Data Exchange (ETDEWEB)
Czinner, Viktor G., E-mail: czinner.viktor@wigner.mta.hu [Laboratory of Physics, College of Science and Technology, Nihon University, 274-8501 Narashinodai, Funabashi, Chiba (Japan); HAS Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal); Iguchi, Hideo, E-mail: iguchi.h@phys.ge.cst.nihon-u.ac.jp [Laboratory of Physics, College of Science and Technology, Nihon University, 274-8501 Narashinodai, Funabashi, Chiba (Japan)
2016-01-10
Thermodynamic stability of black holes, described by the Rényi 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 Rényi formula.
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.
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.
Quantum black hole wave packet: Average area entropy and temperature dependent width
Directory of Open Access Journals (Sweden)
Aharon Davidson
2014-09-01
Full Text Available A quantum Schwarzschild black hole is described, at the mini super spacetime level, by a non-singular wave packet composed of plane wave eigenstates of the momentum Dirac-conjugate to the mass operator. The entropy of the mass spectrum acquires then independent contributions from the average mass and the width. Hence, Bekenstein's area entropy is formulated using the 〈mass2〉 average, leaving the 〈mass〉 average to set the Hawking temperature. The width function peaks at the Planck scale for an elementary (zero entropy, zero free energy micro black hole of finite rms size, and decreases Doppler-like towards the classical limit.
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...
Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
Bañados, Máximo; Zanelli, Jorge; 10.1103/PhysRevLett.72.957
2009-01-01
The Euclidean black hole has topology $\\Re^2 \\times {\\cal S}^{d-2}$. It is shown that -in Einstein's theory- the deficit angle of a cusp at any point in $\\Re^2$ and the area of the ${\\cal S}^{d-2}$ are canonical conjugates. The black hole entropy emerges as the Euler class of a small disk centered at the horizon multiplied by the area of the ${\\cal S}^{d-2}$ there.These results are obtained through dimensional continuation of the Gauss-Bonnet theorem. The extension to the most general action yielding second order field equations for the metric in any spacetime dimension is given.
First Quantum Correction to Dirac Entropy for Rotating U(1)(×)U(1) Dilaton Black Hole
Institute of Scientific and Technical Information of China (English)
高长军; 沈有根
2002-01-01
The first quantum correction to rotating U(1)(×)U(1) dilaton black hole entropy is calculated by using the improved brick-wall model. We propose not to consider the superradiant mode for the reason that fermion fields do not display superradiance. We found that the nonsuperradiant mode does contribute exactly the first quantum correction to the non-extreme black hole entropy. Moreover, our cut-off Newman-Penrose e which does not require an angular cut-off is independent of angle. As for the extreme black hole, we found that its entropy is zero.
Entropy production, viscosity bounds and bumpy black holes
Hartnoll, Sean; Ramirez, David; Santos, Jorge
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 te...
Entropy of non-extremal STU black holes: the F-invariant unveiled
Sárosi, Gábor
2016-01-01
We find a manifestly U-duality invariant formula for the Bekenstein-Hawking entropy of the most general 4 dimensional, stationary, asymptoticaly flat, non-extremal STU black holes constructed recently by Chow and Comp\\`ere. The expression is entirely in terms of asymptotic charges. It involves the "scalar charges" of the black hole which still need to be solved in terms of the dyonic charges and the mass. We discuss how the formula reduces to some of the known results as the Klauza-Klein black hole and the dilute gas limit of Cveti\\v{c} and Larsen. We give the expected generalization to an $E_{7(7)}$ invariant in the case of maximal $\\mathcal{N}=8$ supergravity.
Banerjee, Nabamita; Mandal, Ipsita; Sen, Ashoke
2009-07-01
Macroscopic entropy of an extremal black hole is expected to be determined completely by its near horizon geometry. Thus two black holes with identical near horizon geometries should have identical macroscopic entropy, and the expected equality between macroscopic and microscopic entropies will then imply that they have identical degeneracies of microstates. An apparent counterexample is provided by the 4D-5D lift relating BMPV black hole to a four dimensional black hole. The two black holes have identical near horizon geometries but different microscopic spectrum. We suggest that this discrepancy can be accounted for by black hole hair — degrees of freedom living outside the horizon and contributing to the degeneracies. We identify these degrees of freedom for both the four and the five dimensional black holes and show that after their contributions are removed from the microscopic degeneracies of the respective systems, the result for the four and five dimensional black holes match exactly.
Banerjee, Nabamita; Sen, Ashoke
2009-01-01
Macroscopic entropy of an extremal black hole is expected to be determined completely by its near horizon geometry. Thus two black holes with identical near horizon geometries should have identical macroscopic entropy, and the expected equality between macroscopic and microscopic entropies will then imply that they have identical degeneracies of microstates. An apparent counterexample is provided by the 4D-5D lift relating BMPV black hole to a four dimensional black hole. The two black holes have identical near horizon geometries but different microscopic spectrum. We suggest that this discrepancy can be accounted for by black hole hair, -- degrees of freedom living outside the horizon and contributing to the degeneracies. We identify these degrees of freedom for both the four and the five dimensional black holes and show that after their contributions are removed from the microscopic degeneracies of the respective systems, the result for the four and five dimensional black holes match exactly.
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.
Wavefunction of a black hole and the dynamical origin of entropy
Barvinsky, A O; Zelnikov, A I
1995-01-01
Recently it was proposed to explain the dynamical origin of the entropy of a black hole by identifying its dynamical degrees of freedom with states of quantum fields propagating in the black-hole's interior. The present paper contains the further development of this approach. The no-boundary proposal (analogous to the Hartle-Hawking no-boundary proposal in quantum cosmology) is put forward for defining the wave function of a black hole. This wave function is a functional on the configuration space of physical fields (including the gravitational one) on the three-dimensional space with the Einstein-Rosen bridge topology.It is shown that in the limit of small perturbations on the Kruskal background geometry the no-boundary wave function coincides with the Hartle-Hawking vacuum state. The invariant definition of inside and outside modes is proposed. The density matrix describing the internal state of a black hole is obtained by averaging over the outside modes. This density matrix is used to define the entropy o...
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.
Wang, Peng; Ying, Shuxuan
2015-01-01
We compute the black hole horizon entanglement entropy for a massless scalar field in the brick wall model by incorporating the minimal length. Taking the minimal length effects on the occupation number $n(\\omega,l)$ and the Hawking temperature into consideration, we obtain the leading UV divergent term and the subleading logarithmic term in the entropy. The leading divergent term scales with the horizon area. The subleading logarithmic term is the same as that in the usual brick wall model without the minimal length.
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.
Entropy correction of charged black hole via fermions tunneling beyond semi-classical approximation
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Motivated by the idea of tunneling beyond semi-classical approximation of Majhi et al., we discuss entropy correction of Dirac particles tunneling from the Reissner-Nordstrm black hole with a global monopole. To get the corrections correctly, we regard the proportionality constants of quantum correction terms to the semi-classical term of action as the inverse of the square of the Planck Length but not that of the Planck Mass. Our study shows that corrections to the Bekenstein-Hawking entropy, namely the logarithmic term and the inverse area term, may be reproduced as the quantum effect is considered.
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.
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 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.
Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy
Andrianopoli, Laura; Ferrara, Sergio
1998-01-01
In these lectures we give a geometrical formulation of N-extended supergravities which generalizes N=2 special geometry of N=2 theories. In all these theories duality symmetries are related to the notion of "flat symplectic bundles" and central charges may be defined as "sections" over these bundles. Attractor points giving rise to "fixed scalars" of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.
Lemos, José P. S.; Minamitsuji, Masato; Zaslavskii, Oleg B.
2017-02-01
In a (2 +1 )-dimensional spacetime with a negative cosmological constant, the thermodynamics and the entropy of an extremal rotating thin shell, i.e., an extremal rotating ring, are investigated. The outer and inner regions with respect to the shell are taken to be the Bañados-Teitelbom-Zanelli (BTZ) spacetime and the vacuum ground state anti-de Sitter spacetime, respectively. By applying the first law of thermodynamics to the extremal thin shell, one shows that the entropy of the shell is an arbitrary well-behaved function of the gravitational area A+ alone, S =S (A+). When the thin shell approaches its own gravitational radius r+ and turns into an extremal rotating BTZ black hole, it is found that the entropy of the spacetime remains such a function of A+, both when the local temperature of the shell at the gravitational radius is zero and nonzero. It is thus vindicated by this analysis that extremal black holes, here extremal BTZ black holes, have different properties from the corresponding nonextremal black holes, which have a definite entropy, the Bekenstein-Hawking entropy S (A+)=A/+4G , where G is the gravitational constant. It is argued that for extremal black holes, in particular for extremal BTZ black holes, one should set 0 ≤S (A+)≤A/+4G;i.e., the extremal black hole entropy has values in between zero and the maximum Bekenstein-Hawking entropy A/+4 G . Thus, rather than having just two entropies for extremal black holes, as previous results have debated, namely, 0 and A/+4 G , it is shown here that extremal black holes, in particular extremal BTZ black holes, may have a continuous range of entropies, limited by precisely those two entropies. Surely, the entropy that a particular extremal black hole picks must depend on past processes, notably on how it was formed. A remarkable relation between the third law of thermodynamics and the impossibility for a massive body to reach the velocity of light is also found. In addition, in the procedure, it
Quantum corrected Friedmann equations from loop quantum black holes entropy-area relation
Silva, C A S
2015-01-01
The Friedmann equations govern the evolution of space in homogeneous and isotropic models of the universe within the context of general relativity. Such equations can be derived by using Clausius relation to the apparent horizon of Friedmann-Robertson-Walker (FRW) universe, in which entropy is assumed to be proportional to its horizon area \\cite{Cai:2005ra}. Such demonstration follows the spirit of the results obtained by Jacobson that assuming the proportionality between entropy and horizon area, demonstrated that the spacetime can be viewed as a gas of atoms with a related entropy given by the Bekenstein-Hawking formula and the Einstein equation is a equation of state of this gas \\cite{Jacobson:1995ab}. Loop Quantum Gravity is a theory that propose a way to model the atomic behavior of spacetime. One recent prediction of this theory is the existence of sub-Planckian black holes called self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modif...
Statistical Entropy and Superradiance in 2+1 Dimensional Acoustic Black Holes
Kim, W T; Yoon, M S; Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok
2005-01-01
We study ``draining bathtub'' as an acoustic analogue of a three-dimensional rotating black hole. Rotating fluid near the sonic horizon necessarily gives rise to the superradiant modes, which are partially responsible for the thermodynamic quantities in this rotating vortex-like hole. Using the recently suggested thin-layer method overcoming some difficulties from the well-known brick-wall method, we explicitly calculate the free energy of the system by treating the superradiance carefully and obtain the desirable entropy formula.
A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi entropy
Energy Technology Data Exchange (ETDEWEB)
Biró, Tamás S., E-mail: biro.tamas@wigner.mta.hu [HAS Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Czinner, Viktor G., E-mail: czinner.viktor@wigner.mta.hu [HAS Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, H-1525 Budapest, P.O. Box 49 (Hungary); Centro de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057 Braga (Portugal)
2013-11-04
By regarding the Hawking–Bekenstein entropy of Schwarzschild black hole horizons as a non-extensive Tsallis entropy, its formal logarithm, the Rényi entropy, is considered. The resulting temperature – horizon radius relation has the same form as the one obtained from a (3+1)-dimensional black hole in anti-de Sitter space using the original entropy formula. In both cases the temperature has a minimum. A semi-classical estimate of the horizon radius at this minimum leads to a Bekenstein bound for the q-parameter in the Rényi entropy of micro black holes (q⩾1+2/π{sup 2}), which is surprisingly close to fitted q-parameters of cosmic ray spectra and power-law distribution of quarks coalescing to hadrons in high energy accelerator experiments.
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...
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.
Israel, Werner
This chapter reviews the conceptual developments on black hole thermodynamics and the attempts to determine the origin of black hole entropy in terms of their horizon area. The brick wall model and an operational approach are discussed. An attempt to understand at the microlevel how the quantum black hole acquires its thermal properties is included. The chapter concludes with some remarks on the extension of these techniques to describing the dynamical process of black hole evaporation.
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...
BPS spectrum of the five-brane and black hole entropy
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. [Amsterdam Univ. (Netherlands). Mathematics Inst.; Verlinde, E. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.]|[Rijksuniversiteit Utrecht (Netherlands). Inst. voor Theoretische Fysica; Verlinde, H. [Amsterdam Univ. (Netherlands). Inst. voor Theoretische Fysica]|[Princeton Univ., NJ (United States). Joseph Henry Labs.
1997-02-17
We propose a formulation of 11-dimensional M-theory in terms of five-branes with closed strings on their world-volume. We use this description to construct the complete spectrum of BPS states in compactifications to six and five dimensions. We compute the degeneracy for fixed charge and find it to be in accordance with U-duality (which in our formulation is manifest in six dimensions) and the statistical entropy formula of the corresponding black hole. We also briefly comment on the compactification to four dimensions. (orig.).
BPS spectrum of the five-brane and black hole entropy
Dijkgraaf, R; Verlinde, Herman L
1997-01-01
We propose a formulation of 11-dimensional M-theory in terms of five-branes with closed strings on their world-volume. We use this description to construct the complete spectrum of BPS states in compactifications to six and five dimensions. We compute the degeneracy for fixed charge and find it to be in accordance with U-duality (which in our formulation is manifest in six dimensions) and the statistical entropy formula of the corresponding black hole. We also briefly comment on the four-dimensional case.
Dehghani, M. H.; Pourhasan, R.; Mann, R. B.
2011-01-01
We investigate modifications of the Lifshitz black hole solutions due to the presence of Maxwell charge in higher dimensions for arbitrary $z$ and any topology. We find that the behaviour of large black holes is insensitive to the topology of the solutions, whereas for small black holes significant differences emerge. We generalize a relation previously obtained for neutral Lifshitz black branes, and study more generally the thermodynamic relationship between energy, entropy, and chemical pot...
Quasinormal Modes of Charged Dilaton Black Holes and Their Entropy Spectra
Sakalli, I.
2013-08-01
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 (QNMs) of the CDBH by considering small perturbations around its horizon. By using the highly damped QNM in the process prescribed by Maggiore, we obtain the quantum entropy and area spectra of these black holes (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 ɛ is the double of Bekenstein's result. The possible reason of this discrepancy is also discussed.
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...
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.
Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant
Garattini, Remo
2011-01-01
Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.
Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant
Garattini, Remo
2012-07-01
Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.
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.
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.
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)
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.
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Setare, M.R., E-mail: rezakord@ipm.ir; Adami, H., E-mail: hamed.adami@yahoo.com
2016-01-15
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.
Institute of Scientific and Technical Information of China (English)
Li Gu-Qiang
2005-01-01
The divergences at all levels for the statistical enytropy of a plane symmetry black hole arising from the massless Dirac field are considered using the brick-wall model. It is shown that if we ignore the usual contribution from the vacuum surrounding the system, then the statistical entropy consists of two paarts: one is the linearly divergent term which has the geometric character, the other consists of two logarithmically divergent terms which are not proportional to the surface area of the horizon. The entropy of the Dirac field on extremal plane symmetry spacetime background has higher divergence than usual.
Enthalpy, geometric volume and logarithmic correction to entropy for van der Waals black hole
Pradhan, Parthapratim
2016-10-01
If the negative cosmological constant is treated as a dynamical pressure and if the volume is its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy. Under these circumtances, a new phenomenon emerges in the context of extended phase space thermodynamics. We examine here these features for the recently discovered van der Waals (VDW) black hole (BH) (Rajagopal A. et al., Phys. Lett. B, 737 (2014) 277) which is analogous to the VDW fluid. We show that the thermodynamic volume is greater than the naive geometric volume. We also show that the 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 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 the Cosmic-Censorship-Inequality for this class of BH. In addition finally, we compute the logarithmic correction to the entropy of this BH due to the quantum fluctuations around the thermal equilibrium.
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.
Helical superconducting black holes.
Donos, Aristomenis; Gauntlett, Jerome P
2012-05-25
We construct novel static, asymptotically five-dimensional anti-de Sitter black hole solutions with Bianchi type-VII(0) symmetry that are holographically dual to superconducting phases in four spacetime dimensions with a helical p-wave order. We calculate the precise temperature dependence of the pitch of the helical order. At zero temperature the black holes have a vanishing entropy and approach domain wall solutions that reveal homogenous, nonisotropic dual ground states with an emergent scaling symmetry.
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.
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. ...
Black Hole Entropy and Superconformal Field Theories on Brane-Antibrane Systems
Halyo, E
2004-01-01
We obtain the enropy of Schwarzschild and charged black holes in D>4 from superconformal gases that live on p=10-D dimensional brane-antibrane systems wrapped on T^p. The preperties of the strongly coupled superconformal theories such as the appearance of hidden dimensions (for p=1,4) and fractional strings (for p=5) are crucial for our results. In all cases, the Schwarzschild radius is given by the transverse fluctuations of the branes and antibranes due to the finite temperature. We show that our results can be generalized to multicharged black holes.
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.
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
Black hole collapse and democratic models
Jansen, Aron; Magán, Javier M.
2016-11-01
We study the evolution of black hole entropy and temperature in collapse scenarios in asymptotically anti-de Sitter spacetime, finding three generic lessons. First, entropy evolution is extensive. Second, at large times, entropy and temperature ring with twice the frequency of the lowest quasinormal mode. Third, the entropy oscillations saturate black hole area theorems in general relativity. The first two features are characteristic of entanglement dynamics in "democratic" models. Solely based on general relativity and the Bekenstein-Hawking entropy formula, our results point to democratic models as microscopic theories of black holes. The third feature can be taken as a prediction for microscopic models of black hole physics.
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...
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 ...
Lepton number, black hole entropy and 10 to the 32 copies of the Standard Model
Kovalenko, Sergey; Schmidt, Ivan
2010-01-01
Lepton number violating processes are a typical problem in theories with a low quantum gravity scale. In this paper we examine lepton number violation (LNV) in theories with a saturated black hole bound on a large number of species. Such theories have been advocated recently as a possible solution to the hierarchy problem and an explanation of the smallness of neutrino masses. Naively one would expect black holes to introduce TeV scale LNV operators, thus generating unacceptably large rates of LNV processes. We show, however, that this does not happen in this scenario due to a complicated compensation mechanism between contributions of different Majorana neutrino states to these processes. As a result rates of LNV processes are extremely small and far beyond experimental reach, at least for the left-handed neutrino states.
Visser, M
1999-01-01
Acoustic propagation in a moving fluid provides a conceptually clean and powerful analogy for understanding black hole physics. As a teaching tool, the analogy is useful for introducing students to both General Relativity and fluid mechanics. As a research tool, the analogy helps clarify what aspects of the physics are kinematics and what aspects are dynamics. In particular, Hawking radiation is a purely kinematical effect, whereas black hole entropy is intrinsically dynamical. Finally, I discuss the fact that with present technology acoustic Hawking radiation is almost experimentally testable.
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.
Thermodynamics of Accelerating Black Holes.
Appels, Michael; Gregory, Ruth; Kubizňák, David
2016-09-23
We address a long-standing problem of describing the thermodynamics of an 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.
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.
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...
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...
A note on the black hole remnant
Xiang, Li
2006-01-01
Analyzing the tunneling probability of a Schwarzschild black hole with a negative log-area correction to Bekenstein-Hawking entropy, I argue that this correction may be closely related to a black hole remnant. The value for the minimal black hole mass is also discussed.
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
Charged Black Holes in New Massive Gravity
Ghodsi, Ahmad; Moghadassi, Mohammad
2010-01-01
We construct charged black hole solutions to three-dimensional New Massive Gravity (NMG), by adding electromagnetic Maxwell and Chern-Simons actions. We find charged black holes in the form of warped AdS_3 and "log" solutions in specific critical point. The entropy, mass and angular momentum of these black holes are computed.
The fuzzball proposal for black holes
Skenderis, K.; Taylor, M.
2008-01-01
The fuzzball proposal states that associated with a black hole of entropy S, there are expS horizon-free non-singular solutions that asymptotically look like the black hole but generically differ from the black hole up to the horizon scale. These solutions, the fuzzballs, are considered to be the bl
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.
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.
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.
Thermodynamics of Born-Infeld black holes
Chemissany, Wissam A.; de Roo, Mees; Panda, Sudhakar
2008-01-01
We discuss the horizon structure for Born-Infeld black holes in the context of Einstein-Born-Infeld gravity. We show that the entropy function formalism agrees with a direct calculation of the entropy. With the entropy function formalism we also obtain the entropy when an axion-dilaton system as wel
Supersymmetric black holes in string theory
Energy Technology Data Exchange (ETDEWEB)
Mohaupt, T. [Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL (United Kingdom)
2007-05-15
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 with the topological string, mainly from the supergravity perspective. We summarize the state of art and discuss various open questions and problems. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
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.)
Mathur, Samir D
2012-01-01
The black hole information paradox forces us into a strange situation: we must find a way to break the semiclassical approximation in a domain where no quantum gravity effects would normally be expected. Traditional quantizations of gravity do not exhibit any such breakdown, and this forces us into a difficult corner: either we must give up quantum mechanics or we must accept the existence of troublesome `remnants'. In string theory, however, the fundamental quanta are extended objects, and it turns out that the bound states of such objects acquire a size that grows with the number of quanta in the bound state. The interior of the black hole gets completely altered to a `fuzzball' structure, and information is able to escape in radiation from the hole. The semiclassical approximation can break at macroscopic scales due to the large entropy of the hole: the measure in the path integral competes with the classical action, instead of giving a subleading correction. Putting this picture of black hole microstates ...
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.
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. ...
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.
Entanglement entropy and mutual information production rates in acoustic black holes.
Giovanazzi, Stefano
2011-01-07
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.
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.
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.
Kerr black hole thermodynamical fluctuations
Pavon, D.; Rubi, J. M.
1985-04-01
The near-equilibrium thermodynamical (TD) fluctuations of a massive rotating uncharged Kerr black hole immersed in a uniformly corotating radiation bath at its temperature are investigated theoretically, generalizing Schwarzschild-black-hole analysis of Pavon and Rubi(1983), based on Einstein fluctuation theory. The correlations for the energy and angular moment fluctuations and the second moments of the other TD parameters are obtained, and the generalized second law of black-hole TD and the Bekenstein (1975) interpretation of black-hole entropy are seen as functioning well in this case. A local-stability criterion and relation for TD equilibrium between the Kerr hole and its own radiation in the flat-space-time limit are derived, and a restriction between C and Lambda is deduced.
5D Black Holes and Matrix Strings
Dijkgraaf, R; Verlinde, Herman L
1997-01-01
We derive the world-volume theory, the (non)-extremal entropy and background geometry of black holes and black strings constructed out of the NS IIA fivebrane within the framework of matrix theory. The CFT description of strings propagating in the black hole geometry arises as an effective field theory.
5D black holes and matrix strings
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. [Amsterdam Univ. (Netherlands). Dept. of Mathematics; Verlinde, E. [TH-Division, CERN, CH-1211 Geneva 23 (Switzerland)]|[Institute for Theoretical Physics, University of Utrecht, 3508 TA Utrecht (Netherlands); Verlinde, H. [Institute for Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam (Netherlands)
1997-11-24
We derive the world-volume theory, the (non)-extremal entropy and background geometry of black holes and black strings constructed out of the NS IIA 5-brane within the framework of matrix theory. The CFT description of strings propagating in the black hole geometry arises as an effective field theory. (orig.). 38 refs.
5D black holes and matrix strings
Dijkgraaf, Robbert; Verlinde, Erik; Verlinde, Herman
1997-02-01
We derive the world-volume theory, the (non)-extremal entropy and background geometry of black holes and black strings constructed out of the NS IIA 5-brane within the framework of matrix theory. The CFT description of strings propagating in the black hole geometry arises as an effective field 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.
Dias, G A S; Dias, Goncalo A. S.; Lemos, Jose' P. S.
2006-01-01
A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic compact and oriented horizons, in D spacetime dimensions, is performed. These black holes live in an anti-de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a 2+(D-2) dimensional reduction, where the (D-2) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recover...
Dokuchaev, V I
2012-01-01
We consider test planet and photon orbits of the third kind inside a black hole, which are stable, periodic and neither come out of the black hole nor terminate at the singularity. Interiors of supermassive black holes may be inhabited by advanced civilizations living on planets with the third-kind orbits. In principle, one can get information from the interiors of black holes by observing their white hole counterparts.
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.
Entropy of a self-gravitating electrically charged thin shell and the black hole limit
Lemos, José P S; Zaslavski, Oleg B
2015-01-01
A static self-gravitating electrically charged spherical thin shell embedded in a (3+1)-dimensional spacetime is used to study the thermodynamic and entropic properties of the corresponding spacetime. Inside the shell, the spacetime is flat, outside it is Reissner-Nordstr\\"om, and this establishes the energy density, the pressure, and the electric charge in the shell. Imposing that the shell is at a given local temperature and that the first law of thermodynamics holds on the shell one can find the integrability conditions for the temperature and for the thermodynamic electric potential, the thermodynamic equilibrium states, and the thermodynamic stability conditions. Through the integrability conditions and the first law of thermodynamics an expression for the shell's entropy can be calculated. It is found that the shell's entropy is a function of the shell's gravitational and Cauchy radii alone. A plethora of sets of temperature and electric potential equations of state can be given. One set of equations of...
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.
THE ENTROPY OF A KIM BLACK HOLE AND THE NERNST THEOREM%Kim黑洞熵与能斯特定理
Institute of Scientific and Technical Information of China (English)
赵仁; 张丽春
2001-01-01
We start with Klein-Gordon equation on the background of the Kim black hole and calculate the free energy and entropy of a scalar field by the brick-wall method. It is shown that the entropy is not only related to the area of an outer horizon but also is a function of inner horizon's area. Taking some appr oximation, we can obtain that the entropy only is proportional to the area of an outer horizon. Further more, the entropy expressed by location parameter of the outer and inner horizon approaches zero, when the radiation temperature of a black hole approaches zero. This satisfies the Nernst theorem. It can be taken as Planck absolute entropy of a black hole.%从Kim 时空背景下的 Klein-Gordon 方程出发，利用 brick-wall 方法计算标量场的自由能和熵.得到标量场的熵不仅与黑洞的外视界面积有关,而且也是内视界面积的函数.所得结论,当取某种近似时,可得到熵只与外视界面积成正比的关系.并且表明,用内外视界位置参量表达的熵,在黑洞辐射温度趋于绝对零度时,黑洞的熵也趋于零,它满足能斯特定理,可视为黑洞的普朗克绝对熵.
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.
The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons
Pithis, Andreas G A
2012-01-01
This letter presents a new argument for considering the states of the quantum isolated horizon as distinguishable. It is claimed that only if the states are distinguishable, the entropy is an extensive quantity and can be well-defined. To show this, the comparison with a classical ideal gas system is explicitly given, whose statistical description makes only sense, if an additional 1/N! is included in the state counting, curing the Gibbs paradox. The difference with the statistical description of a quantum isolated horizon is elaborated, to make the claim evident. This letter is a product of the author's diploma thesis.
Moss, I. G.; Shiiki, N.; Winstanley, E.
2000-01-01
Charged black hole solutions with pion hair are discussed. These can be\\ud used to study monopole black hole catalysis of proton decay.\\ud There also exist\\ud multi-black hole skyrmion solutions with BPS monopole behaviour.
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.
Wijers, R.A.M.J.
1996-01-01
Introduction Distinguishing neutron stars and black holes Optical companions and dynamical masses X-ray signatures of the nature of a compact object Structure and evolution of black-hole binaries High-mass black-hole binaries Low-mass black-hole binaries Low-mass black holes Formation of black holes
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.
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
Partition functions for supersymmetric black holes
Manschot, J.
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
Nonthermal nature of extremal Kerr black holes
Rothman, T
2000-01-01
Liberati, Rothman and Sonego have recently showed that objects collapsing into extremal Reissner-Nordstrom black holes do not behave as thermal objects at any time in their history. In particular, a temperature, and hence thermodynamic entropy, are undefined for them. I demonstrate that the analysis goes through essentially unchanged for Kerr black holes.
Letelier, P S; Letelier, Patricio S.; Oliveira, Samuel R.
1998-01-01
The C-metric is revisited and global interpretation of some associated spacetimes are studied in some detail. Specially those with two event horizons, one for the black hole and another for the acceleration. We found that the spacetime fo an accelerated Schwarzschild black hole is plagued by either conical singularities or lack of smoothness and compactness of the black hole horizon. By using standard black hole thermodynamics we show that accelerated black holes have higher Hawking temperature than Unruh temperature. We also show that the usual upper bound on the product of the mass and acceleration parameters (<1/sqrt(27)) is just a coordinate artifact. The main results are extended to accelerated Kerr black holes. We found that they are not changed by the black hole rotation.
Black Holes: The Membrane Viewpoint
Thorne, Kip S.
Contents: I. Introduction: 1. Overview of the membrane viewpoint. 2. History of research on the membrane viewpoint. II. The 3+1 split of spacetime: 1. ZAMOs and the 3+1 split of the metric. 2. Gravitoelectric and gravitomagnetic fields. 3. 3+1 split of electrodynamics. III. Stretching the horizon and black-hole thermodynamics: 1. Macdonald's vibrating magnetic field problem. 2. Stretching the horizon. 3. The entropy of a black hole. 4. The thermodynamics and mechanics of a black hole. IV. Electrodynamics of the stretched horizon: 1. The laws of Gauss, Ampere, Ohm, and charge conservation. 2. Lorentz force and ohmic dissipation in the stretched horizon. V. Some electromagnetic model problems: 1. Charge separation in the stretched horizon. 2. Black hole as a resistor in an electric circuit. 3. Black hole as the rotor in an electric motor. 4. Rotating hole immersed in a time-independent, vacuum magnetic field. 5. Magnetized, rotating hole as a battery for an external circuit. VI. Astrophysical applications of the membrane formalism. VII. Conclusion.
The KKW Generalized Analysis for a Magnetic Stringy Black Hole
Radinschi, I.
2004-01-01
We apply the Keski-Vakkuri, Kraus and Wilczek (KKW) generalized analysis to a magnetic stringy black hole solution to compute its temperature and entropy. The solution that we choose in the Einstein-dilaton-Maxwell theory is the dual solution known as the magnetic black hole solution. Our results show that the expressions of the temperature and entropy of this non-Schwarzschild-type black hole are not the Hawking temperature and the Bekenstein-Hawking entropy, respectively. In addition, the e...
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 ...
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.
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.
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.
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.
Ho, Pei-Ming
2017-04-01
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.
Einstein-Euler-Heisenberg Theory and Charged Black Holes
Ruffini, Remo; Xue, She-Sheng
2013-01-01
Taking into account the Euler-Heisenberg effective Lagrangian of one-loop nonperturbative Quantum Electrodynamics (QED) contributions, we formulate the Einstein-Euler-Heisenberg theory, and study the solutions of non-rotating black holes with electric and magnetic charges in spherical geometry. In the limit of strong and weak electromagnetic fields of black holes, we calculate the black hole horizon radius, area, and total energy up to the leading order of QED corrections, and discuss the black hole irreducible mass, entropy, and maximally extractable energy as well as the Christodoulou-Ruffini mass formula. We find that these black hole quantities receive the QED corrections, in comparison with their counterparts in the Reissner-Nortstr\\"om solution. The QED corrections show the screening effect on black hole electric charges and the paramagnetic effect on black hole magnetic charges. As a result, the black hole horizon area, irreducible mass, and entropy increase, however the black hole total energy and max...
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.
Perturbing supersymmetric black hole
Onozawa, H; Mishima, T; Ishihara, H; Onozawa, Hisashi; Okamura, Takashi; Mishima, Takashi; Ishihara, Hideki
1996-01-01
An investigation of the perturbations of the Reissner-Nordstr\\"{o}m black hole in the N=2 supergravity is presented. In the extreme case, the black hole responds to the perturbation of each field in the same manner. This is possibly because we can match the modes of the graviton, gravitino, and photon using supersymmetry transformations.
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.
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.
Stornaiolo, C
2002-01-01
In this letter we propose the existence of low density black holes and discuss its compatibility with the cosmological observations. The origin of these black holes can be traced back to the collapse of long wavelength cosmological perturbations during the matter dominated era, when the densities are low enough to neglect any internal and thermal pressure. By introducing a threshold density $\\hat{\\rho}$ above which pressure and non-gravitational interactions become effective, we find the highest wavelength for the perturbations that can reach an equilibrium state instead of collapsing to a black hole. The low density black holes introduced here, if they exist, can be observed through weak and strong gravitational lensing effects. Finally we observe that we obtained here a cosmological model which is capable to explain in a qualitative way the void formation together with the value $\\Omega=1$. But we remark that it needs to be improved by considering non spherical symmetric black holes.
Primordial Black Hole Baryogenesis
Baumann, D; Turok, N G; Baumann, Daniel; Steinhardt, Paul J.; Turok, Neil
2007-01-01
We reconsider the possibility that the observed baryon asymmetry was generated by the evaporation of primordial black holes that dominated the early universe. We present a simple derivation showing that the baryon asymmetry is insensitive to the initial black hole density and the cosmological model but is sensitive to the temperature-dependence of the CP and baryon-violating (or lepton-violating) interactions. We also consider the possibility that black holes stop evaporating and form Planck-mass remnants that act as dark matter. We show that primordial black holes cannot simultaneously account for both the observed baryon asymmetry and the (remnant) dark matter density unless the magnitude of CP violation is much greater than expected from most particle physics models. Finally, we apply these results to ekpyrotic/cyclic models, in which primordial black holes may form when branes collide. We find that obtaining the observed baryon asymmetry is compatible with the other known constraints on parameters.
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.
Carlip, S
2014-01-01
The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox.
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.
Dumb holes: analogues for black holes.
Unruh, W G
2008-08-28
The use of sonic analogues to black and white holes, called dumb or deaf holes, to understand the particle production by black holes is reviewed. The results suggest that the black hole particle production is a low-frequency and low-wavenumber process.
Better late than never: information retrieval from black holes.
Braunstein, Samuel L; Pirandola, Stefano; Życzkowski, Karol
2013-03-08
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.
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.
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.
Smarr formula for Lovelock black holes: A Lagrangian approach
Liberati, Stefano; Pacilio, Costantino
2016-04-01
The mass formula for black holes can be formally expressed in terms of a Noether charge surface integral plus a suitable volume integral, for any gravitational theory. The integrals can be constructed as an application of Wald's formalism. We apply this formalism to compute the mass and the Smarr formula for static Lovelock black holes. Finally, we propose a new prescription for Wald's entropy in the case of Lovelock black holes, which takes into account topological contributions to the entropy functional.
Quantum loop corrections of charged dS black hole
Naji, J
2016-01-01
In this paper, a charged black hole in de Sitter space considered and logarithmic corrected entropy used to study thermodynamics. Logarithmic corrections of entropy comes from thermal fluctuations which plays role of quantum loop corrections. In that case we are able to study the effect of quantum loop on the black hole thermodynamics and statistics. As black hole is a gravitational object, so it helps to obtain some information about the quantum gravity.
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.
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.
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.
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
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.
MacGibbon, Jane H; Linnemann, J T; Marinelli, S S; Stump, D; Tollefson, K
2015-01-01
Primordial Black Holes (PBHs) are of interest in many cosmological contexts. PBHs lighter than about 1012 kg are predicted to be directly detectable by their Hawking radiation. This radiation should produce both a diffuse extragalactic gamma-ray background from the cosmologically-averaged distribution of PBHs and gamma-ray burst signals from individual light black holes. The Fermi, Milagro, Veritas, HESS and HAWC observatories, in combination with new burst recognition methodologies, offer the greatest sensitivity for the detection of such black holes or placing limits on their existence.
Central charge for the Schwarzschild black hole
Ropotenko, K.
2016-12-01
Proceeding in exactly the same way as in the derivation of the temperature of a dual CFT for the extremal black hole in the Kerr/CFT correspondence, it is found that the temperature of a chiral, dual CFT for the Schwarzschild black hole is T = 1/2π. Comparing Cardy’s formula with the Bekenstein-Hawking entropy and using T, it is found that the central charge for the Schwarzschild black hole is of the form c = 12Jin, where Jin is the intrinsic angular momentum of the black hole, Jin = A/8πG. It is shown that the central charge for any four-dimensional (4D) extremal black hole is of the same form. The possible universality of this form is briefly discussed.
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.
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.
Gregory, Ruth
2008-01-01
In these lectures, I give an introduction to and overview of braneworlds and black holes in the context of warped compactifications. I first describe the general paradigm of braneworlds, and introduce the Randall-Sundrum model. I discuss braneworld gravity, both using perturbation theory, and also non perturbative results. I then discuss black holes on the brane, the obstructions to finding exact solutions, and ways of tackling these difficulties. I describe some known solutions, and conclude with some open questions and controversies.
Pelletier, G.
2004-01-01
Black Holes generate a particular kind of environments dominated by an accretion flow which concentrates a magnetic field. The interplay of gravity and magnetism creates this paradoxical situation where relativistic ejection is allowed and consequently high energy phenomena take place. Therefore Black Holes, which are very likely at the origin of powerfull astrophysical phenomena such as AGNs, micro- quasars and GRBs where relativistic ejections are observed, are at the heart of high energy a...
Exact Results for the BTZ Black Hole
Birmingham, Daniel; Sen, S; Birmingham, Danny; Sachs, Ivo; Sen, Siddhartha
2001-01-01
In this review, we summarize exact results for the three-dimensional BTZ black hole. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. In particular, we study the formation of the black hole by point particle collisions, leading to an exact analytic determination of the Choptuik scaling parameter. We also show that a `No Hair Theorem' follows immediately from a mathematical theorem of hyperbolic geometry, due to Sullivan. A microscopic understanding of the Bekenstein-Hawking entropy, and decay rate for massless scalars, is shown to follow from standard results of conformal field theory.
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…
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.
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.
Centrella, Joan
2009-05-01
The final merger of two black holes is expected to be the strongest gravitational wave source for ground-based interferometers such as LIGO, VIRGO, and GEO600, as well as the space-based LISA. Observing these sources with gravitational wave detectors requires that we know the radiation waveforms they emit. And, when the black holes merge in the presence of gas and magnetic fields, various types of electromagnetic signals may also be produced. Since these mergers take place in regions of extreme gravity, we need to solve Einstein's equations of general relativity on a computer. For more than 30 years, scientists have tried to compute black hole mergers using the methods of numerical relativity. The resulting computer codes have been plagued by instabilities, causing them to crash well before the black holes in the binary could complete even a single orbit. Within the past few years, however, this situation has changed dramatically, with a series of remarkable breakthroughs. This talk will focus on new simulations that are revealing the dynamics and waveforms of binary black hole mergers, and their applications in gravitational wave detection, testing general relativity, and astrophysics.
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...
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.
Pelletier, G
2004-01-01
Black Holes generate a particular kind of environments dominated by an accretion flow which concentrates a magnetic field. The interplay of gravity and magnetism creates this paradoxical situation where relativistic ejection is allowed and consequently high energy phenomena take place. Therefore Black Holes, which are very likely at the origin of powerfull astrophysical phenomena such as AGNs, micro- quasars and GRBs where relativistic ejections are observed, are at the heart of high energy astrophysics. The combination of General Relativity and Magneto-HydroDynamics (MHD) makes theory difficult; however great pionneers opened beautiful tracks in the seventies and left important problems to be solved for the next decades. These lectures will present the status of these issues. They have a tutorial aspect together with critical review aspect and contain also some new issues. Most of these lectures has been presented at the "School on Black Hole in the Universe" at Cargese, in May 2003.
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.
Centrella, Joan
2012-01-01
The final merger of two black holes is expected to be the strongest source of gravitational waves for both ground-based detectors such as LIGO and VIRGO, as well as future. space-based detectors. Since the merger takes place in the regime of strong dynamical gravity, computing the resulting gravitational waveforms requires solving the full Einstein equations of general relativity on a computer. For many years, numerical codes designed to simulate black hole mergers were plagued by a host of instabilities. However, recent breakthroughs have conquered these instabilities and opened up this field dramatically. This talk will focus on.the resulting 'gold rush' of new results that is revealing the dynamics and waveforms of binary black hole mergers, and their applications in gravitational wave detection, testing general relativity, and astrophysics
Lasota, Jean-Pierre
2015-01-01
This is an introduction to models of accretion discs around black holes. After a presentation of the non-relativistic equations describing the structure and evolution of geometrically thin accretion discs we discuss their steady-state solutions and compare them to observation. Next we describe in detail the thermal-viscous disc instability model and its application to dwarf novae for which it was designed and its X-ray irradiated-disc version which explains the soft X--ray transients, i.e. outbursting black-hole low-mass X-ray binaries. We then turn to the role of advection in accretion flow onto black holes illustrating its action and importance with a toy model describing both ADAFs and slim discs. We conclude with a presentation of the general-relativistic formalism describing accretion discs in the Kerr space-time.
Black hole gravitohydromagnetics
Punsly, Brian
2008-01-01
Black hole gravitohydromagnetics (GHM) is developed from the rudiments to the frontiers of research in this book. GHM describes plasma interactions that combine the effects of gravity and a strong magnetic field, in the vicinity (ergosphere) of a rapidly rotating black hole. This topic was created in response to the astrophysical quest to understand the central engines of radio loud extragalactic radio sources. The theory describes a "torsional tug of war" between rotating ergospheric plasma and the distant asymptotic plasma that extracts the rotational inertia of the black hole. The recoil from the struggle between electromagnetic and gravitational forces near the event horizon is manifested as a powerful pair of magnetized particle beams (jets) that are ejected at nearly the speed of light. These bipolar jets feed large-scale magnetized plasmoids on scales as large as millions of light years (the radio lobes of extragalactic radio sources). This interaction can initiate jets that transport energy fluxes exc...
Fender, Rob; Heywood, Ian
2013-01-01
Starting from the assumption that there is a large population (> 10^8) of isolated, stellar-mass black holes (IBH) distributed throughout our galaxy, we consider the detectable signatures of accretion from the interstellar medium (ISM) that may be associated with such a population. We simulate the nearby (radius 250 pc) part of this population, corresponding to the closest ~35 000 black holes, using current best estimates of the mass distribution of stellar mass black holes combined with two models for the velocity distribution of stellar-mass IBH which bracket likely possibilities. We distribute this population of objects appropriately within the different phases of the ISM and calculate the Bondi-Hoyle accretion rate, modified by a further dimensionless efficiency parameter \\lambda. Assuming a simple prescription for radiatively inefficient accretion at low Eddington ratios, we calculate the X-ray luminosity of these objects, and similarly estimate the radio luminosity from relations found empirically for b...
Black Holes as Effective Geometries
Balasubramanian, Vijay; El-Showk, Sheer; Messamah, Ilies
2008-01-01
Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective t...
Fractal black holes and information
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, University of Alexandria, Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)
2006-07-15
If nature is fractal as it evidently is, at classical resolution and if it is suspected to also be fractal at the quantum resolution as it is now a days generally believed to be, then we must have over looked at least two points or so in our physical model building of mini black holes. To start with at such ultra high resolution, the mini black hole geometry must be a fractal. Consequently we have zero volume and only a fractal surface area. Second because we cannot take the differential limit for the -bar {sub p}{sup 2} covering the transfinite surface area, there will be many gaps between the (-bar {sub p}){sup 2} tilings. In other words we must introduce transfinite corrections to the final result. Proceeding this way the information entropy unit of a black hole should be a=I=(7+{phi}{sup 3})(10){sup -66}cm{sup 2}=7.23606799(10){sup -66}cm{sup 2}The nearest classical result to the above is that obtained by Gerard 't Hoofta=I=(0.724)(10){sup -65}cm{sup 2}The paper ends with a general discussion of E-infinity theory and its possible relation with 't Hooft's holographic principle and his gluons-quark strings.
Dokuchaev, Vyacheslav
2013-11-01
It is considered the test planet and photon orbits of the third kind inside the black hole (BH), which are stable, periodic and neither come out the BH nor terminate at the central singularity. Interiors of the supermassive BHs may be inhabited by advanced civilizations living on the planets with the third kind orbits. In principle, one can get information from the interiors of BHs by observing their white hole counterparts.
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.
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.
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.
Hennigar, Robie A; Mann, Robert B; Tjoa, Erickson
2017-01-13
We present what we believe is the first example of a "λ-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 anti-de Sitter 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.
Characterizing Black Hole Mergers
Baker, John; Boggs, William Darian; Kelly, Bernard
2010-01-01
Binary black hole mergers are a promising source of gravitational waves for interferometric gravitational wave detectors. Recent advances in numerical relativity have revealed the predictions of General Relativity for the strong burst of radiation generated in the final moments of binary coalescence. We explore features in the merger radiation which characterize the final moments of merger and ringdown. Interpreting the waveforms in terms of an rotating implicit radiation source allows a unified phenomenological description of the system from inspiral through ringdown. Common features in the waveforms allow quantitative description of the merger signal which may provide insights for observations large-mass black hole binaries.
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.
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.)
Infinite volume of noncommutative black hole wrapped by finite surface
Zhang, Baocheng; You, Li
2017-02-01
The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein-Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.
Weak Gravity Conjecture and Extremal Black Holes
Cottrell, William; Soler, Pablo
2016-01-01
Motivated by the desire to improve our understanding of the Weak Gravity Conjecture, we compute the one-loop correction of charged particles to the geometry and entropy of extremal black holes in 4d. Contrary to expectations, we find that loops of massive charged particles can radically alter the classical black hole geometry and that fermion loops provide evidence for the necessity of the `magnetic' WGC cutoff. The corrections are reduced when supersymmetry is present, and disappear in ${\\cal N}=4$ supergravity. We further provide some speculative arguments that in a theory with only sub-extremal particles, classical Reisner-Nordstrom black holes actually possess an infinite microcanonical entropy, though only a finite amount is visible to an external observer.
Black hole thermodynamics under the microscope
Falls, Kevin
2012-01-01
A coarse-grained version of the effective action is used to study the thermodynamics of black holes, interpolating from largest to smallest masses. The physical parameter of the black hole are linked to the running couplings by thermodynamics, and the corresponding equation of state includes quantum corrections for temperature, specific heat, and entropy. If quantum gravity becomes asymptotically safe, the state function predicts conformal scaling in the limit of small horizon area, and bounds on black hole mass and temperature. A metric-based derivation for the equation of state, and quantum corrections to the thermodynamical, statistical, and phenomenological definition of entropy are also given. Further implications and limitations of our study are discussed.
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.)
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.
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.
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.
The fuzzball proposal for black holes
Energy Technology Data Exchange (ETDEWEB)
Skenderis, Kostas [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018XE Amsterdam (Netherlands)], E-mail: skenderi@science.uva.nl; Taylor, Marika [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018XE Amsterdam (Netherlands)], E-mail: taylor@science.uva.nl
2008-10-15
The fuzzball proposal states that associated with a black hole of entropy S, there are expShorizon-free non-singular solutions that asymptotically look like the black hole but generically differ from the black hole up to the horizon scale. These solutions, the fuzzballs, are considered to be the black hole microstates, while the original black hole represents the average description of the system. The purpose of this report is to review current evidence for the fuzzball proposal, emphasizing the use of AdS/CFT methods in developing and testing the proposal. In particular, we discuss the status of the proposal for 2 and 3 charge black holes in the D1-D5 system, presenting new derivations and streamlining the discussion of their properties. Results to date support the fuzzball proposal, but further progress is likely to require going beyond the supergravity approximation and sharpening the definition of a 'stringy fuzzball'. We outline how the fuzzball proposal could resolve longstanding issues in black hole physics, such as Hawking radiation and information loss. Our emphasis throughout is on connecting different developments and identifying open problems and directions for future research.
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.
Bambi, Cosimo
2013-01-01
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 ...
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.
Neitzke, A.; Pioline, B.; Vandoren, S.
2007-01-01
Motivated by black hole physics in N = 2,D = 4 supergravity, we study the geometry of quaternionic-K¨ahler manifolds Mobtained by the c-map construction from projective special Kähler manifolds Ms. Improving on earlier treatments, we compute the Käahler potentials on the twistor space Z and Swann sp
Gregory, Ruth; Wills, Danielle
2013-01-01
A Kerr black hole sporting cosmic string hair is studied in the context of the abelian Higgs model vortex. It is shown that a such a system displays much richer phenomenology than its static Schwarzschild or Reissner--Nordstrom cousins, for example, the rotation generates a near horizon `electric' field. In the case of an extremal rotating black hole, two phases of the Higgs hair are possible: Large black holes exhibit standard hair, with the vortex piercing the event horizon. Small black holes on the other hand, exhibit a flux-expelled solution, with the gauge and scalar field remaining identically in their false vacuum state on the event horizon. This solution however is extremely sensitive to confirm numerically, and we conjecture that it is unstable due to a supperradiant mechanism similar to the Kerr-adS instability. Finally, we compute the gravitational back reaction of the vortex, which turns out to be far more nuanced than a simple conical deficit. While the string produces a conical effect, it is con...
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.
Simulations of coalescing black holes
Janiuk, Agnieszka
2016-01-01
We describe the methods and results of numerical simulations of coalescing black holes. The simulation in dynamical spacetime covers the inspiral, merger, and ringdown phases. We analyze the emission of gravitational waves and properties of a black hole being the merger product. We discuss the results in the context of astrophysical environment of black holes that exist in the Universe.
"Exotic" black holes with torsion
2013-01-01
In the context of three-dimensional gravity with torsion, the concepts of standard and "exotic" Banados-Teitelboim-Zanelli black holes are generalized by going over to black holes with torsion. This approach provides a unified insight into thermodynamics of black holes, with or without torsion.
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
Energy Technology Data Exchange (ETDEWEB)
Nicolini, Piero, E-mail: nicolini@fias.uni-frankfurt.de [Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Institut für Theoretische Physik, J.W. Goethe-Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); Singleton, Douglas, E-mail: dougs@csufresno.edu [Department of Physics, California State University, Fresno, CA 93740-8031 (United States); Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, Distrito Federal, 04510 (Mexico)
2014-11-10
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.
The Foaming Three-Charge Black Hole
Bena, Iosif; Wang, Chih-Wei; Nicholas P. Warner(Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, U.S.A.)
2006-01-01
We find a very large set of smooth horizonless geometries that have the same charges and angular momenta as the five-dimensional, maximally-spinning, three-charge, BPS black hole (J^2 = Q^3). Our solutions are constructed using a four-dimensional Gibbons-Hawking base space that has a very large number of two-cycles. The entropy of our solutions is proportional to Q^(1/2). In the same class of solutions we also find microstates corresponding to zero-entropy black rings, and these are related t...
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.
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.
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.
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)
Roldán-Molina, A; Nunez, Alvaro S; Duine, R A
2017-02-10
We show that the interaction between the spin-polarized current and the magnetization dynamics can be used to implement black-hole and white-hole horizons for magnons-the quanta of oscillations in the magnetization direction in magnets. We consider three different systems: easy-plane ferromagnetic metals, isotropic antiferromagnetic metals, and easy-plane magnetic insulators. Based on available experimental data, we estimate that the Hawking temperature can be as large as 1 K. We comment on the implications of magnonic horizons for spin-wave scattering and transport experiments, and for magnon entanglement.
Roldán-Molina, A.; Nunez, Alvaro S.; Duine, R. A.
2017-02-01
We show that the interaction between the spin-polarized current and the magnetization dynamics can be used to implement black-hole and white-hole horizons for magnons—the quanta of oscillations in the magnetization direction in magnets. We consider three different systems: easy-plane ferromagnetic metals, isotropic antiferromagnetic metals, and easy-plane magnetic insulators. Based on available experimental data, we estimate that the Hawking temperature can be as large as 1 K. We comment on the implications of magnonic horizons for spin-wave scattering and transport experiments, and for magnon entanglement.
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.
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.
Faccio, Daniele; Lamperti, Marco; Leonhardt, Ulf
2012-01-01
Using numerical simulations we show how to realise an optical black hole laser, i.e. an amplifier formed by travelling refractive index perturbations arranged so as to trap light between a white and a black hole horizon. The simulations highlight the main features of these lasers: the growth inside the cavity of positive and negative frequency modes accompanied by a weaker emission of modes that occurs in periodic bursts corresponding to the cavity round trips of the trapped modes. We then highlight a new regime in which the trapped mode spectra broaden until the zero-frequency points on the dispersion curve are reached. Amplification at the horizon is highest for zero-frequencies, therefore leading to a strong modification of the structure of the trapped light. For sufficiently long propagation times, lasing ensues only at the zero-frequency modes.
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.
The black hole information problem beyond quantum theory
Mueller, Markus P; Dahlsten, Oscar C O
2012-01-01
The origin of black hole entropy and the black hole information problem provide important clues for trying to piece together a quantum theory of gravity. Thus far, discussions on this topic have mostly assumed that in a consistent theory of gravity and quantum mechanics, quantum theory will be unmodified. Here, we examine the black hole information problem in the context of generalisations of quantum theory. In particular, we examine black holes in the setting of generalised probabilistic theories, in which quantum theory and classical probability theory are special cases. We compute the time it takes information to escape a black hole, assuming that information is preserved. We find that under some very general assumptions, the arguments of Page (that information should escape the black hole after half the Hawking photons have been emitted), and the black-hole mirror result of Hayden and Preskill (that information can escape quickly) need to be modified. The modification is determined entirely by what we cal...
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.
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.
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.
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...
Clément, G; Leygnac, C; Clement, Gerard; Gal'tsov, Dmitri; Leygnac, Cedric
2003-01-01
We present new solutions to Einstein-Maxwell-dilaton-axion (EMDA) gravity in four dimensions describing black holes which asymptote to the linear dilaton background. In the non-rotating case they can be obtained as the limiting geometry of dilaton black holes. The rotating solutions (possibly endowed with a NUT parameter) are constructed using a generating technique based on the Sp(4,R) duality of the EMDA system. In a certain limit (with no event horizon present) our rotating solutions coincide with supersymmetric Israel-Wilson-Perjes type dilaton-axion solutions. In presence of an event horizon supersymmetry is broken. The temperature of the static black holes is constant, and their mass does not depend on it, so the heat capacity is zero. We investigate geodesics and wave propagation in these spacetimes and find superradiance in the rotating case. Because of the non-asymptotically flat nature of the geometry, certain modes are reflected from infinity, in particular, all superradiant modes are confined. Thi...
Black hole chemistry: thermodynamics with Lambda
Kubizňák, David; Mann, Robert B.; Teo, Mae
2017-03-01
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 extending the AdS/CFT dictionary in this setting, discuss the connections with horizon thermodynamics, applications to Lifshitz spacetimes, and outline possible future directions in this field.
Relic Radiation from an Evaporating Black Hole
Farley, A N St J
2007-01-01
We present a non-string-theoretic calculation of the microcanonical entropy of relic integer-spin Hawking radiation -- at fixed total energy $E$. The only conserved macroscopic quantity is the total energy $E$ (the total energy of the relic radiation). Data for a boundary-value approach, with massless, integer-spin perturbations, are set on initial and final space-like hypersurfaces. In the resulting 1-dimensional statistical-mechanics problem, the real part of the (complex) time separation at spatial infinity, $T = {\\mid}T{\\mid}\\exp(-i\\delta), \\delta >0$, is the variable conjugate to the total energy. We count the number of weak-field configurations on the final space-like hypersurface with energy $E$. One recovers the Cardy formula and the Bekenstein-Hawking entropy, if Re(T) is of the order of the black-hole life- time, leading to a statistical interpretation of black-hole entropy. The microcanonical entropy includes a logarithmic correction to the black-hole area law, which is {\\it universal} (independent...
Shiiki, N; Shiiki, Noriko; Sawado, Nobuyuki
2005-01-01
This paper is intended to give a review of the recent developments on black holes with Skyrme hair. The Einstein-Skyrme system is known to possess black hole solutions with Skyrme hair. The spherically symmetric black hole skyrmion with B=1 was the first discovered counter example of the no-hair conjecture for black holes. Recently we found the B=2 axially symmetric black hole skyrmion. In this system, the black hole at the center of the skyrmion absorbs the baryon number partially, leaving fractional charge outside the horizon. Therefore the baryon number is no longer conserved. We examine the B=1, 2 black hole solutions in detail in this paper. The model has a natural extension to the gauged version which can describe monopole black hole skyrmions. Callan and Witten discussed the monopole catalysis of proton decay within the Skyrme model. We apply the idea to the Einstein-Maxwell-Skyrme system and obtain monopole black hole skyrmions. Remarkably there exist multi-black hole skyrmion solutions in which the g...
Curiel, Erik
2014-01-01
In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is `no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of "tempe...
Requardt, Manfred
2009-01-01
We present strong arguments that the deep structure of the quantum vacuum contains a web of microscopic wormholes or short-cuts. We develop the concept of wormhole spaces and show that this web of wormholes generate a peculiar array of long-range correlations in the patterns of vacuum fluctuations on the Planck scale. We conclude that this translocal structure represents the common cause for both the BH-entropy-area law, the more general holographic principle and the entanglement phenomena in quantum theory. In so far our approach exhibits a common structure which underlies both gravity and quantum theory on a microscopic scale. A central place in our analysis is occupied by a quantitative derivation of the distribution laws of microscopic wormholes in the quantum vacuum. This makes it possible to address a number of open questions and controversial topics in the field of quantum gravity.
Geometry of black hole spacetimes
Andersson, Lars; Blue, Pieter
2016-01-01
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds. The Kerr model of a rotating black hole in vacuum is expected to be unique and stable. The problem of proving these fundamental facts provides the background for the material presented in these notes. Among the many topics which are relevant for the uniqueness and stability problems are the theory of fields on black hole spacetimes, in particular for gravitational perturbations of the Kerr black hole, and more generally, the study of nonlinear field equations in the presence of trapping. The study of these questions requires tools from several different fields, including Lorentzian geometry, hyperbolic differential equations and spin geometry, which are all relevant to the black hole stability problem.
Thermodynamics of higher dimensional black holes
Energy Technology Data Exchange (ETDEWEB)
Accetta, F.S.; Gleiser, M.
1986-05-01
We discuss the thermodynamics of higher dimensional black holes with particular emphasis on a new class of spinning black holes which, due to the increased number of Casimir invariants, have additional spin degrees of freedom. In suitable limits, analytic solutions in arbitrary dimensions are presented for their temperature, entropy, and specific heat. In 5 + 1 and 9 + 1 dimensions, more general forms for these quantities are given. It is shown that the specific heat for a higher dimensional black hole is negative definite if it has only one non-zero spin parameter, regardless of the value of this parameter. We also consider equilibrium configurations with both massless particles and massive string modes. 16 refs., 3 figs.
Black Holes and Quantumness on Macroscopic Scales
Flassig, D; Wintergerst, N
2012-01-01
It has recently been suggested that black holes may be described as condensates of weakly interacting gravitons at a critical point, exhibiting strong quantum effects. In this paper, we study a model system of attractive bosons in one spatial dimension which is known to undergo a quantum phase transition. We demonstrate explicitly that indeed quantum effects are important at the critical point, even if the number of particles is macroscopic. Most prominently, we evaluate the entropy of entanglement between different momentum modes and observe it to become maximal at the critical point. Furthermore, we explicitly see that the leading entanglement is between long wavelength modes and is hence a feature independent of ultraviolet physics. If applicable to black holes, our findings substantiate the conjectured breakdown of semiclassical physics even for large black holes. This can resolve long standing mysteries, such as the information paradox and the no-hair theorem.
Quantization of rotating linear dilaton black holes
Sakalli, I
2014-01-01
In this paper, we firstly prove that the adiabatic invariant quantity, which is commonly used in the literature for quantizing the rotating black holes (BHs) is fallacious. We then show how its corrected form should be. The main purpose of this paper is to study the quantization of 4-dimensional rotating linear dilaton black hole (RLDBH) spacetime describing with an action, which emerges in the Einstein-Maxwell-Dilaton-Axion (EMDA) theory. The RLDBH spacetime has a non-asymptotically flat (NAF) geometry. They reduces to the linear dilaton black hole (LDBH) metric when vanishing its rotation parameter "a". While studying its scalar perturbations, it is shown that the Schr\\"odinger-like wave equation around the event horizon reduces to a confluent hypergeometric differential equation. Then the associated complex frequencies of the quasinormal modes (QNMs) are computed. By using those QNMs in the true definition of the rotational adiabatic invariant quantity, we obtain the quantum spectra of entropy/area for the...
Origin of supermassive black holes
Dokuchaev, V. I.; Eroshenko, Yu. N.; Rubin, S G
2007-01-01
The origin of supermassive black holes in the galactic nuclei is quite uncertain in spite of extensive set of observational data. We review the known scenarios of galactic and cosmological formation of supermassive black holes. The common drawback of galactic scenarios is a lack of time and shortage of matter supply for building the supermassive black holes in all galaxies by means of accretion and merging. The cosmological scenarios are only fragmentarily developed but propose and pretend to...
Lasota, Jean-Pierre
2015-01-01
This is an introduction to models of accretion discs around black holes. After a presentation of the non-relativistic equations describing the structure and evolution of geometrically thin accretion discs we discuss their steady-state solutions and compare them to observation. Next we describe in detail the thermal-viscous disc instability model and its application to dwarf novae for which it was designed and its X-ray irradiated-disc version which explains the soft X--ray transients, i.e. ou...
Visser, Matt; Volovik, Grigory E
2009-01-01
Physicists are pondering on the possibility of simulating black holes in the laboratory by means of various "analog models". These analog models, typically based on condensed matter physics, can be used to help us understand general relativity (Einstein's gravity); conversely, abstract techniques developed in general relativity can sometimes be used to help us understand certain aspects of condensed matter physics. This book contains 13 chapters - written by experts in general relativity, particle physics, and condensed matter physics - that explore various aspects of this two-way traffic.
Black holes and the multiverse
Garriga, Jaume; Vilenkin, Alexander; Zhang, Jun
2016-02-01
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse.
How black holes saved relativity
Prescod-Weinstein, Chanda
2016-02-01
While there have been many popular-science books on the historical and scientific legacy of Albert Einstein's general theory of relativity, a gap exists in the literature for a definitive, accessible history of the theory's most famous offshoot: black holes. In Black Hole, the science writer Marcia Bartusiak aims for a discursive middle ground, writing solely about black holes at a level suitable for both high-school students and more mature readers while also giving some broader scientific context for black-hole research.
Thermodynamics of Schwarzschild-Beltrami-de Sitter Black Hole
Liu, Hang
2016-01-01
In this paper, we investigate the thermodynamical properties of Schwarzschild-Beltrami-de Sitter black hole introduced by Mu-Lin Yan \\textit{et al.} in 2013 by introducing inertial Beltrami coordinates to traditional non-inertial Schwarzschild-de Sitter metric which is the exact static spherical symmetry solution of Einstein equation with a positive cosmological constant $\\Lambda$. Based on this new metric, we compute entropy on all horizons and we give the entropy bound of the black hole. Hawking temperatures are calculated by considering a perturbation to entropy relations due to that there does not exist a killing horizon where the surface gravity related to Hawking temperature is defined well in this inertial coordinates. We also get the Smarr relations and the first law of thermodynamics. We find that the Schwarzschild-Beltrami-de Sitter black hole has almost the same thermodynamical properties as Schwarzschild-de Sitter black hole in the comparison between their corresponding thermodynamical quantities,...
Directory of Open Access Journals (Sweden)
I. Cabrera-Munguia
2015-04-01
Full Text Available A 6-parametric asymptotically flat exact solution, describing a two-body system of asymmetric black dyons, is studied. The system consists of two unequal counterrotating Kerr–Newman black holes, endowed with electric and magnetic charges which are equal but opposite in sign, separated by a massless strut. The Smarr formula is generalized in order to take into account their contribution to the mass. The expressions for the horizon half-length parameters σ1 and σ2, as functions of the Komar parameters and of the coordinate distance, are displayed, and the thermodynamic properties of the two-body system are studied. Furthermore, the seven physical parameters satisfy a simple algebraic relation which can be understood as a dynamical scenario, in which the physical properties of one body are affected by the ones of the other body.
2002-10-01
Star Orbiting Massive Milky Way Centre Approaches to within 17 Light-Hours [1] Summary An international team of astronomers [2], lead by researchers at the Max-Planck Institute for Extraterrestrial Physics (MPE) , has directly observed an otherwise normal star orbiting the supermassive black hole at the center of the Milky Way Galaxy. Ten years of painstaking measurements have been crowned by a series of unique images obtained by the Adaptive Optics (AO) NAOS-CONICA (NACO) instrument [3] on the 8.2-m VLT YEPUN telescope at the ESO Paranal Observatory. It turns out that earlier this year the star approached the central Black Hole to within 17 light-hours - only three times the distance between the Sun and planet Pluto - while travelling at no less than 5000 km/sec . Previous measurements of the velocities of stars near the center of the Milky Way and variable X-ray emission from this area have provided the strongest evidence so far of the existence of a central Black Hole in our home galaxy and, implicitly, that the dark mass concentrations seen in many nuclei of other galaxies probably are also supermassive black holes. However, it has not yet been possible to exclude several alternative configurations. In a break-through paper appearing in the research journal Nature on October 17th, 2002, the present team reports their exciting results, including high-resolution images that allow tracing two-thirds of the orbit of a star designated "S2" . It is currently the closest observable star to the compact radio source and massive black hole candidate "SgrA*" ("Sagittarius A") at the very center of the Milky Way. The orbital period is just over 15 years. The new measurements exclude with high confidence that the central dark mass consists of a cluster of unusual stars or elementary particles, and leave little doubt of the presence of a supermassive black hole at the centre of the galaxy in which we live . PR Photo 23a/02 : NACO image of the central region of the Milky Way
Black hole microstates in anti-de Sitter space
Shaghoulian, Edgar
2016-11-01
We extend a recently derived higher-dimensional Cardy formula to include angular momenta, which we use to obtain the Bekensten-Hawking entropy of anti-de Sitter black branes, compactified rotating branes, and large Schwarzschild/Kerr black holes. This is the natural generalization of Strominger's microscopic derivation of the Banados-Teitelboim-Zanelli black hole entropy to higher dimensions. We propose an extension to include U (1 ) charge, which agrees with the Bekenstein-Hawking entropy of large Reissner-Nordstrom/Kerr-Newman black holes at high temperature. We extend the results to an arbitrary hyperscaling-violation exponent (this captures the case of black D p -branes as a subclass) and reproduce logarithmic corrections.
Microstate solutions from black hole deconstruction
Raeymaekers, Joris
2015-01-01
We present a new family of asymptotic AdS_3 x S^2 solutions to eleven dimensional supergravity compactified on a Calabi-Yau threefold. They originate from the backreaction of S^2-wrapped M2-branes, which play a central role in the deconstruction proposal for the microscopic interpretation of the D4-D0 black hole entropy. We show that they are free of possible pathologies such as closed timelike curves and discuss their holographic interpretation.
Stability and thermodynamics of brane black holes
Energy Technology Data Exchange (ETDEWEB)
Abdalla, E. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, SP (Brazil)]. E-mail: eabdalla@fma.if.usp.br; Cuadros-Melgar, B. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, SP (Brazil)]. E-mail: bertha@fma.if.usp.br; Pavan, A.B. [Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, 05315-970 Sao Paulo, SP (Brazil)]. E-mail: alan@fma.if.usp.br; Molina, C. [Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo, Av. Arlindo Bettio 1000, CEP 03828-000 Sao Paulo, SP (Brazil)]. E-mail: cmolina@usp.br
2006-09-18
We consider scalar and axial gravitational perturbations of black hole solutions in brane world scenarios. We show that perturbation dynamics is surprisingly similar to the Schwarzschild case with strong indications that the models are stable. Quasinormal modes and late-time tails are discussed. We also study the thermodynamics of these scenarios verifying the universality of Bekenstein's entropy bound as well as the applicability of 't Hooft's brickwall method.
Stability and Thermodynamics of Brane Black Holes
Energy Technology Data Exchange (ETDEWEB)
Abdalla, E; Cuadros-Melgar, B; Pavan, A B [Instituto de Fisica, Universidade de Sao Paulo, C.P.66.318, CEP 05315-970, Sao Paulo (Brazil); Molina, C [Escola de Artes, Ciencias e Humanidades, Universidade de Sao Paulo Av. Arlindo Bettio 1000, CEP 03828-000, Sao Paulo-SP (Brazil)
2007-05-15
We consider scalar and axial gravitational perturbations of black hole solutions in brane world scenarios. We show that perturbation dynamics is surprisingly similar to the Schwarzschild case with strong indications that the models are stable. Quasinormal modes and late-time tails are discussed. We also study the thermodynamics of these scenarios verifying the universality of Bekenstein's entropy bound as well as the applicability of 't Hooft's brickwall method.
Noncanonical Phase-Space Noncommutative Black Holes
Bastos, Catarina; Dias, Nuno; Prata, João
2012-01-01
In this contribution we present a noncanonical phase-space noncommutative (NC) extension of a Kantowski Sachs (KS) cosmological model to describe the interior of a Schwarzschild black hole (BH). We evaluate the thermodynamical quantities inside this NC Schwarzschild BH and compare with the well known quantities. We find that for a NCBH the temperature and entropy have the same mass dependence as the Hawking quantities for a Schwarzschild BH.
Thermodynamic products for Sen black hole
Energy Technology Data Exchange (ETDEWEB)
Pradhan, Parthapratim [Vivekananda Satavarshiki Mahavidyalaya (Affiliated to Vidyasagar University), Department of Physics, Manikpara, West Bengal (India)
2016-03-15
We investigate the properties of inner and outer horizon thermodynamics of Sen black hole (BH) both in Einstein frame (EF) and string frame (SF). We also compute area (or entropy) product, area (or entropy) sum of the said BH in EF as well as SF. In the EF, we observe that the area (or entropy) product is universal, whereas area (or entropy) sum is not universal. On the other hand, in the SF, area (or entropy) product and area (or entropy) sum don't have any universal behaviour because they all are depends on Arnowitt-Deser-Misner (ADM) mass parameter. We also verify that the first law is satisfied at the Cauchy horizon as well as event horizon (EH). In addition, we also compute other thermodynamic products and sums in the EF as well as in the SF. We further compute the Smarr mass formula and Christodoulou's irreducible mass formula for Sen BH. Moreover, we compute the area bound and entropy bound for both the horizons. The upper area bound for EH is actually the Penrose like inequality, which is the first geometric inequality in BHs. Furthermore, we compute the central charges of the left and right moving sectors of the dual CFT in Sen/CFT correspondence using thermodynamic relations. These thermodynamic relations on the multi-horizons give us further understanding the microscopic nature of BH entropy (both interior and exterior). (orig.)
Massive particle radiation from Gibbons-Maeda black hole
Institute of Scientific and Technical Information of China (English)
Fang Heng-Zhong
2010-01-01
This paper investigated the massive particle radiation from Gibbous-Maeda black hole by using a semi-classical method. The calculations showed that, if the self-gravitation of the radiated particle is taken into account, the radiation spectrum deviates from exact black body spectrum and the rate of tunneling equals precisely the exponent of the difference of the black hole entropies before and after emission. The conclusion supports the viewpoint of information conservation.
Belloni, T M
2016-01-01
The last two decades have seen a great improvement in our understand- ing of the complex phenomenology observed in transient black-hole binary systems, especially thanks to the activity of the Rossi X-Ray Timing Explorer satellite, com- plemented by observations from many other X-ray observatories and ground-based radio, optical and infrared facilities. Accretion alone cannot describe accurately the intricate behavior associated with black-hole transients and it is now clear that the role played by different kinds of (often massive) outflows seen at different phases of the outburst evolution of these systems is as fundamental as the one played by the accretion process itself. The spectral-timing states originally identified in the X-rays and fundamentally based on the observed effect of accretion, have acquired new importance as they now allow to describe within a coherent picture the phenomenology observed at other wave- length, where the effects of ejection processes are most evident. With a particular focu...
Holographic Principle of Black Holes in Brans-Dicke Theory
Chen, C Y; Chen, Chi-Yi; Shen, You-Gen
2003-01-01
We consider the general situation of type-I stationary solutions of black holes in Brans-Dicke theory and investigate their statistical entropies by using the brick wall model. Compare with a generalized entropy formula derived from their thermodynamical evolution by Kang, We get the ultimate scenario of black holes entropies in Brans-Dicke theory. For further considering the bound of holographic principle, we obtain a new constraint on parameters in this type solution read as $2Q-\\chi=2$, which corresponds to $\\omega=-{3/2}$.
Landauer Transport Model for Hawking Radiation from a Black Hole
Nation, P D; Nori, Franco
2010-01-01
We investigate the Hawking radiation energy and entropy flow rates from a black hole viewed as a one-dimensional (1D) Landauer transport process. The conformal symmetry in the near-horizon region leads directly to radiation rates that are identical to those of a single 1D quantum channel connected to a thermal reservoir at the Hawking temperature. The particle statistics independence of the 1D energy and entropy currents is applied to a black hole radiating into vacuum as well as one near thermal equilibrium with its environment. The Hawking radiation entropy production ratio is also examined.
Detailed black hole state counting in loop quantum gravity
Agullo, Ivan; Barbero G., J. Fernando; Borja, Enrique F.; Diaz-Polo, Jacobo; Villaseñor, Eduardo J. S.
2010-10-01
We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step toward obtaining the behavior of entropy in the asymptotic (large horizon area) regime.
Detailed black hole state counting in loop quantum gravity
Agullo, Ivan; Borja, Enrique F; Diaz-Polo, Jacobo; Villaseñor, Eduardo J S; 10.1103/PhysRevD.82.084029
2011-01-01
We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step towards obtaining the behavior of entropy in the asymptotic (large horizon area) regime.
Astrophysical Black Holes in the Physical Universe
Zhang, Shuang-Nan
2010-01-01
In this chapter I focus on asking and answering the following questions: (1) What is a black hole? Answer: There are three types of black holes, namely mathematical black holes, physical black holes and astrophysical black holes. An astrophysical black hole, with mass distributed within its event horizon but not concentrated at the singularity point, is not a mathematical black hole. (2) Can astrophysical black holes be formed in the physical universe? Answer: Yes, at least this can be done with gravitational collapse. (3) How can we prove that what we call astrophysical black holes are really black holes? Answer: Finding direct evidence of event horizon is not the way to go. Instead I propose five criteria which meet the highest standard for recognizing new discoveries in experimental physics and observational astronomy. (4) Do we have sufficient evidence to claim the existence of astrophysical black holes in the physical universe? Answer: Yes, astrophysical black holes have been found at least in some galac...
Area spectrum of slowly rotating black holes
2010-01-01
We investigate the area spectrum for rotating black holes which are Kerr and BTZ black holes. For slowly rotating black holes, we use the Maggiore's idea combined with Kunstatter's method to derive their area spectra, which are equally spaced.
Black holes in an expanding universe.
Gibbons, Gary W; Maeda, Kei-ichi
2010-04-02
An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state (P = w rho with -1 black hole temperature.
DEFF Research Database (Denmark)
Vestergaard, Marianne
2004-01-01
The applicability and apparent uncertainties of the techniques currently available for measuring or estimating black-hole masses in AGNs are briefly summarized.......The applicability and apparent uncertainties of the techniques currently available for measuring or estimating black-hole masses in AGNs are briefly summarized....
ATLAS simulated black hole event
Pequenão, J
2008-01-01
The simulated collision event shown is viewed along the beampipe. The event is one in which a microscopic-black-hole was produced in the collision of two protons (not shown). The microscopic-black-hole decayed immediately into many particles. The colors of the tracks show different types of particles emerging from the collision (at the center).
Nonlinear Electrodynamics and black holes
Breton, N; Breton, Nora; Garcia-Salcedo, Ricardo
2007-01-01
It is addressed the issue of black holes with nonlinear electromagnetic field, focussing mainly in the Born-Infeld case. The main features of these systems are described, for instance, geodesics, energy conditions, thermodynamics and isolated horizon aspects. Also are revised some black hole solutions of alternative nonlinear electrodynamics and its inconveniences.
When Charged Black Holes Merge
Kohler, Susanna
2016-08-01
Most theoretical models assume that black holes arent charged. But a new study shows that mergers of charged black holes could explain a variety of astrophysical phenomena, from fast radio bursts to gamma-ray bursts.No HairThe black hole no hair theorem states that all black holes can be described by just three things: their mass, their spin, and their charge. Masses and spins have been observed and measured, but weve never measured the charge of a black hole and its widely believed that real black holes dont actually have any charge.That said, weve also never shown that black holes dont have charge, or set any upper limits on the charge that they might have. So lets suppose, for a moment, that its possible for a black hole to be charged. How might that affect what we know about the merger of two black holes? A recent theoretical study by Bing Zhang (University of Nevada, Las Vegas) examines this question.Intensity profile of a fast radio burst, a sudden burst of radio emission that lasts only a few milliseconds. [Swinburne Astronomy Productions]Driving TransientsZhangs work envisions a pair of black holes in a binary system. He argues that if just one of the black holes carries charge possibly retained by a rotating magnetosphere then it may be possible for the system to produce an electromagnetic signal that could accompany gravitational waves, such as a fast radio burst or a gamma-ray burst!In Zhangs model, the inspiral of the two black holes generates a global magnetic dipole thats perpendicular to the plane of the binarys orbit. The magnetic flux increases rapidly as the separation between the black holes decreases, generating an increasingly powerful magnetic wind. This wind, in turn, can give rise to a fast radio burst or a gamma-ray burst, depending on the value of the black holes charge.Artists illustration of a short gamma-ray burst, thought to be caused by the merger of two compact objects. [ESO/A. Roquette]Zhang calculates lower limits on the charge
Black holes and the multiverse
Garriga, Jaume; Zhang, Jun
2015-01-01
Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive blac...
Energy Technology Data Exchange (ETDEWEB)
Hubeny, Veronika; Maloney, Alexander; Rangamani, Mukund
2005-02-07
We investigate the geometry of four dimensional black hole solutions in the presence of stringy higher curvature corrections to the low energy effective action. For certain supersymmetric two charge black holes these corrections drastically alter the causal structure of the solution, converting seemingly pathological null singularities into timelike singularities hidden behind a finite area horizon. We establish, analytically and numerically, that the string-corrected two-charge black hole metric has the same Penrose diagram as the extremal four-charge black hole. The higher derivative terms lead to another dramatic effect -- the gravitational force exerted by a black hole on an inertial observer is no longer purely attractive! The magnitude of this effect is related to the size of the compactification manifold.
Entangled black holes as ciphers of hidden information
Braunstein, Samuel L; Zyczkowski, Karol \\
2009-01-01
The black-hole information paradox has fueled a fascinating effort to reconcile the predictions of general relativity and those of quantum mechanics. Gravitational considerations teach us that black holes must trap everything that falls into them. Quantum mechanically the mass of a black hole leaks away as featureless (Hawking) radiation. However, if Hawking's analysis turned out to be accurate then the information would be irretrievably lost and a fundamental axiom of quantum mechanics, that of unitary evolution, would likewise fail. Here we show that the information about the matter that collapses to form a black hole becomes encoded into pure correlations within a tripartite quantum system, the quantum analog of a one-time pad until very late in the evaporation, provided we accept the view that the thermodynamic entropy of a black hole is due to entropy of entanglement. In this view the black hole entropy is primarily due to trans-event horizon entanglement between external modes neighboring the black hole...
Magnetic fields around black holes
Garofalo, David A. G.
Active Galactic Nuclei are the most powerful long-lived objects in the universe. They are thought to harbor supermassive black holes that range from 1 million solar masses to 1000 times that value and possibly greater. Theory and observation are converging on a model for these objects that involves the conversion of gravitational potential energy of accreting gas to radiation as well as Poynting flux produced by the interaction of the rotating spacetime and the electromagnetic fields originating in the ionized accretion flow. The presence of black holes in astrophysics is taking center stage, with the output from AGN in various forms such as winds and jets influencing the formation and evolution of the host galaxy. This dissertation addresses some of the basic unanswered questions that plague our current understanding of how rotating black holes interact with their surrounding magnetized accretion disks to produce the enormous observed energy. Two magnetic configurations are examined. The first involves magnetic fields connecting the black hole with the inner accretion disk and the other involves large scale magnetic fields threading the disk and the hole. We study the effects of the former type by establishing the consequences that magnetic torques between the black hole and the inner accretion disk have on the energy dissipation profile. We attempt a plausible explanation to the observed "Deep Minimum" state in the Seyfert galaxy MCG-6- 30-15. For the latter type of magnetic geometry, we study the effects of the strength of the magnetic field threading the black hole within the context of the cherished Blandford & Znajek mechanism for black hole spin energy extraction. We begin by addressing the problem in the non-relativistic regime where we find that the black hole-threading magnetic field is stronger for greater disk thickness, larger magnetic Prandtl number, and for a larger accretion disk. We then study the problem in full relativity where we show that our
The new thermodynamic relations of multi-horizons black holes
Xu, Wei; Meng, Xin-he
2014-01-01
We present some general entropy and temperature relations of multi-horizons, even of the "virtual" horizon. These relations are related to product, division and sum of entropy and temperature of multi-horizons. We obtain the additional thermodynamic relations for Schwarzschild-(A)dS black holes and Reissner-Nordstr{\\"o}m-(A)dS black holes, which are found to be held for both AdS and dS black holes. Besides, a new dimensionless, mass-independence and $T_+S_+=T_-S_-$ like relation is presented. It seems to be more universal and does not depend on the mass, electric charge and cosmological constant, as it is a constant in both Schwarzschild-(A)dS black holes and Reissner-Nordstr{\\"o}m-(A)dS black holes. This new relation can be expected to link entropy relations via thermodynamics law and Smarr relation of each horizons and be helpful of understanding microscopically the black hole entropy.
The Statistical Mechanics of Black Hole Thermodynamics
Sorkin, R D
1997-01-01
Although we have convincing evidence that a black hole bears an entropy proportional to its surface (horizon) area, the ``statistical mechanical'' explanation of this entropy remains unknown. Two basic questions in this connection are: what is the microscopic origin of the entropy, and why does the law of entropy increase continue to hold when the horizon entropy is included? After a review of some of the difficulties in answering these questions, I propose an explanation of the law of entropy increase which comes near to a proof in the context of the ``semi-classical'' approximation, and which also provides a proof in full quantum gravity under the assumption that the latter fulfills certain natural expectations, like the existence of a conserved energy definable at infinity. This explanation seems to require a fundamental spacetime discreteness in order for the entropy to be consistently finite, and I recall briefly some of the ideas for what the discreteness might be. If such ideas are right, then our know...
Information-carrying Hawking radiation and the number of microstate for a black hole
Cai, Qing-yu; You, Li
2016-01-01
We present a necessary and sufficient condition to falsify whether a Hawking radiation spectrum indicates unitary emission process or not from the perspective of information theory. With this condition, we show the precise values of Bekenstein-Hawking entropies for Schwarzschild black holes and Reissner-Nordstr\\"om black holes can be calculated by counting the microstates of their Hawking radiations. In particular, for the extremal Reissner-Nordstr\\"om black hole, its number of microstate and the corresponding entropy we obtain are found to be consistent with the string theory results. Our finding helps to refute the dispute about the Bekenstein-Hawking entropy of extremal black holes in the semiclassical limit.
Recoiling Black Holes in Quasars
Bonning, E W; Salviander, S
2007-01-01
Recent simulations of merging black holes with spin give recoil velocities from gravitational radiation up to several thousand km/s. A recoiling supermassive black hole can retain the inner part of its accretion disk, providing fuel for a continuing QSO phase lasting millions of years as the hole moves away from the galactic nucleus. One possible observational manifestation of a recoiling accretion disk is in QSO emission lines shifted in velocity from the host galaxy. We have examined QSOs from the Sloan Digital Sky Survey with broad emission lines substantially shifted relative to the narrow lines. We find no convincing evidence for recoiling black holes carrying accretion disks. We place an upper limit on the incidence of recoiling black holes in QSOs of 4% for kicks greater than 500 km/s and 0.35% for kicks greater than 1000 km/s line-of-sight velocity.
A nonsingular rotating black hole
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, Durban (South Africa)
2015-11-15
The spacetime singularities in classical general relativity are inevitable, as predicated by the celebrated singularity theorems. However, it is a general belief that singularities do not exist in Nature and that they are the limitations of the general relativity. In the absence of a welldefined quantum gravity, models of regular black holes have been studied. We employ a probability distribution inspired mass function m(r) to replace the Kerr black hole mass M to represent a nonsingular rotating black hole that is identified asymptotically (r >> k, k > 0 constant) exactly as the Kerr-Newman black hole, and as the Kerr black hole when k = 0. The radiating counterpart renders a nonsingular generalization of Carmeli's spacetime as well as Vaidya's spacetime, in the appropriate limits. The exponential correction factor changing the geometry of the classical black hole to remove the curvature singularity can also be motivated by quantum arguments. The regular rotating spacetime can also be understood as a black hole of general relativity coupled to nonlinear electrodynamics. (orig.)
Rotating black hole and quintessence
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Private Bag 54001, Durban (South Africa)
2016-04-15
We discuss spherically symmetric exact solutions of the Einstein equations for quintessential matter surrounding a black hole, which has an additional parameter (ω) due to the quintessential matter, apart from the mass (M). In turn, we employ the Newman-Janis complex transformation to this spherical quintessence black hole solution and present a rotating counterpart that is identified, for α = -e{sup 2} ≠ 0 and ω = 1/3, exactly as the Kerr-Newman black hole, and as the Kerr black hole when α = 0. Interestingly, for a given value of parameter ω, there exists a critical rotation parameter (a = a{sub E}), which corresponds to an extremal black hole with degenerate horizons, while for a < a{sub E}, it describes a nonextremal black hole with Cauchy and event horizons, and no black hole for a > a{sub E}. We find that the extremal value a{sub E} is also influenced by the parameter ω and so is the ergoregion. (orig.)
Cosmic Intelligence and Black Holes
Lefebvre, V A; Lefebvre, Vladimir A.; Efremov, Yuri N.
2000-01-01
The paper is devoted to a new direction in SETI. After a general discussion of the field, the authors put forth the hypothesis that the black holes may serve as a physical substratum for intelligent beings. This hypothesis is based on four parallels between the brain-psyche system, on the one hand, and black holes, on the other. (1) The descriptions of brain and psyche, in the system brain-psyche, are complementary to each other, as descriptions by internal and external observers of a black hole in Susskind-t'Hooft's schema. (2) There is an aspect of the inner structure of a black hole in Kerr's model of the rotating black hole that is isomorphic to the structure of the human subjective domain in the psychological model of reflexion. (3) Both black holes and the brain-psyche system have a facet which can be represented using thermodynamic concepts. (4) The brain lends itself to a holographic description; as has been recently demonstrated by Susskind, black holes can also be described holographically. The auth...
Quantum mechanics of black holes.
Witten, Edward
2012-08-03
The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.
Orbital resonances around black holes.
Brink, Jeandrew; Geyer, Marisa; Hinderer, Tanja
2015-02-27
We compute the length and time scales associated with resonant orbits around Kerr black holes for all orbital and spin parameters. Resonance-induced effects are potentially observable when the Event Horizon Telescope resolves the inner structure of Sgr A*, when space-based gravitational wave detectors record phase shifts in the waveform during the resonant passage of a compact object spiraling into the black hole, or in the frequencies of quasiperiodic oscillations for accreting black holes. The onset of geodesic chaos for non-Kerr spacetimes should occur at the resonance locations quantified here.
Black holes and Higgs stability
Energy Technology Data Exchange (ETDEWEB)
Tetradis, Nikolaos [Department of Physics, University of Athens,Zographou 157 84 (Greece); Physics Department, Theory Unit, CERN,CH-1211 Geneva 23 (Switzerland)
2016-09-20
We study the effect of primordial black holes on the classical rate of nucleation of AdS regions within the standard electroweak vacuum. We find that the energy barrier for transitions to the new vacuum, which characterizes the exponential suppression of the nucleation rate, can be reduced significantly in the black-hole background. A precise analysis is required in order to determine whether the the existence of primordial black holes is compatible with the form of the Higgs potential at high temperature or density in the Standard Model or its extensions.
The Black Hole Information Problem
Polchinski, Joseph
2016-01-01
The black hole information problem has been a challenge since Hawking's original 1975 paper. It led to the discovery of AdS/CFT, which gave a partial resolution of the paradox. However, recent developments, in particular the firewall puzzle, show that there is much that we do not understand. I review the black hole, Hawking radiation, and the Page curve, and the classic form of the paradox. I discuss AdS/CFT as a partial resolution. I then discuss black hole complementarity and its limitations, leading to many proposals for different kinds of `drama.' I conclude with some recent ideas.
Cho, Inyong
2016-01-01
We investigate black holes formed by static perfect fluid with $p=-\\rho/3$. These represent the black holes in $S_3$ and $H_3$ spatial geometries. There are three classes of black-hole solutions, two $S_3$ types and one $H_3$ type. The interesting solution is the one of $S_3$ type which possesses two singularities. The one is at the north pole behind the horizon, and the other is naked at the south pole. The observers, however, are free from falling to the naked singularity. There are also nonstatic cosmological solutions in $S_3$ and $H_3$, and a singular static solution in $H_3$.
On regular rotating black holes
Torres, R.; Fayos, F.
2017-01-01
Different proposals for regular rotating black hole spacetimes have appeared recently in the literature. However, a rigorous analysis and proof of the regularity of this kind of spacetimes is still lacking. In this note we analyze rotating Kerr-like black hole spacetimes and find the necessary and sufficient conditions for the regularity of all their second order scalar invariants polynomial in the Riemann tensor. We also show that the regularity is linked to a violation of the weak energy conditions around the core of the rotating black hole.
Black Holes: A Traveler's Guide
Pickover, Clifford A.
1998-03-01
BLACK HOLES A TRAVELER'S GUIDE Clifford Pickover's inventive and entertaining excursion beyond the curves of space and time. "I've enjoyed Clifford Pickover's earlier books . . . now he has ventured into the exploration of black holes. All would-be tourists are strongly advised to read his traveler's guide." -Arthur C. Clarke. "Many books have been written about black holes, but none surpass this one in arousing emotions of awe and wonder towards the mysterious structure of the universe." -Martin Gardner. "Bucky Fuller thought big. Arthur C. Clarke thinks big, but Cliff Pickover outdoes them both." -Wired. "The book is fun, zany, in-your-face, and refreshingly addictive." -Times Higher Education Supplement.
Lovelock black holes in a string cloud background
Energy Technology Data Exchange (ETDEWEB)
Lee, Tae-Hun; Baboolal, Dharmanand [University of KwaZulu-Natal, School of Mathematical Sciences, Durban (South Africa); Ghosh, Sushant G. [University of KwaZulu-Natal, School of Mathematical Sciences, Durban (South Africa); Centre for Theoretical Physics, New Delhi (India)
2015-07-15
We present an exact static, spherically symmetric black hole solution to the third-order Lovelock gravity with a string cloud background in seven dimensions for the special case when the second- and third-order Lovelock coefficients are related via α{sub 2}{sup 2} = 3α{sub 3} (≡ α{sup 2}). Further, we examine thermodynamic properties of this black hole to obtain exact expressions for mass, temperature, heat capacity and entropy, and also perform the thermodynamic stability analysis. We see that a string cloud background has a profound influence on the horizon structure, thermodynamic properties, and the stability of black holes. Interestingly the entropy of the black hole is unaffected due to the string cloud background. However, the critical solution for thermodynamic stability is affected by the string cloud background. (orig.)
Lovelock black holes in a string cloud background
Lee, Tae-Hun; Ghosh, Sushant G
2014-01-01
We present an exact static, spherically symmetric black hole solution to the third order Lovelock gravity with a string cloud background in seven dimensions for the special case when the second and third order Lovelock coefficients are related via $\\tilde{\\alpha}^2_2=3\\tilde{\\alpha}_3\\;(\\equiv\\alpha^2)$. Further, we examine thermodynamic properties of this black hole to obtain exact expressions for mass, temperature, entropy and also perform the thermodynamic stability analysis. We see that a string cloud background makes a profound influence on horizon structure, thermodynamic properties and the stability of black holes. Interestingly, the entropy of the black hole is unaffected due to a string cloud background. However, the critical solution for thermodynamic stability is being affected by a string cloud background.
Warped-AdS3 black holes with scalar halo
Giribet, Gaston
2015-01-01
We construct a stretched (aka Warped) Anti-de Sitter black hole in 3 dimensions supported by a real scalar field configuration. The latter is regular everywhere outside and on the horizon. No hair theorems in 3 dimensions demand the matter to be coupled to the curvature in a non-minimal way; however, this coupling can still be of the Horndeski type, i.e. yielding second order field equations similar to those appearing in the context of Galileon theories. These Warped-Anti-de Sitter black holes exhibit interesting thermodynamical properties, such as finite Hawking temperature and entropy. We compute the black hole entropy in the gravity theory and speculate with the possibility of this to admit a microscopic description in terms of a dual (Warped) Conformal Field Theory. We also discuss the inner and outer black hole mechanics.
Black hole state degeneracy in Loop Quantum Gravity
Agullo, Ivan; Fernandez-Borja, Enrique
2008-01-01
The combinatorial problem of counting the black hole quantum states within the Isolated Horizon framework in Loop Quantum Gravity is analyzed. A qualitative understanding of the origin of the band structure shown by the degeneracy spectrum, which is responsible for the black hole entropy quantization, is reached. Even when motivated by simple considerations, this picture allows to obtain analytical expressions for the most relevant quantities associated to this effect.
Black hole state counting in LQG: A number theoretical approach
Agullo, Ivan; Diaz-Polo, Jacobo; Fernandez-Borja, Enrique; Villaseñor, Eduardo J S
2008-01-01
We give a practical method to exactly compute black hole entropy in the framework of Loop Quantum Gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and determine the number of solutions to the projection constraint analytically. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.
Supertranslations and Superrotations at the Black Hole Horizon.
Donnay, Laura; Giribet, Gaston; González, Hernán A; Pino, Miguel
2016-03-04
We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.
van Herck, Walter; Wyder, Thomas
2010-04-01
The enumeration of BPS bound states in string theory needs refinement. Studying partition functions of particles made from D-branes wrapped on algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow trees, we extend the method for computing a refined BPS index, [1]. For certain D-particles, a finite number of microstates, namely polar states, exclusively realized as bound states, determine an entire partition function (elliptic genus). This underlines their crucial importance: one might call them the ‘chromosomes’ of a D-particle or a black hole. As polar states also can be affected by our refinement, previous predictions on elliptic genera are modified. This can be metaphorically interpreted as ‘crossing-over in the meiosis of a D-particle’. Our results improve on [2], provide non-trivial evidence for a strong split attractor flow tree conjecture, and thus suggest that we indeed exhaust the BPS spectrum. In the D-brane description of a bound state, the necessity for refinement results from the fact that tachyonic strings split up constituent states into ‘generic’ and ‘special’ states. These are enumerated separately by topological invariants, which turn out to be partitions of Donaldson-Thomas invariants. As modular predictions provide a check on many of our results, we have compelling evidence that our computations are correct.
Van Herck, Walter
2009-01-01
The enumeration of BPS bound states in string theory needs refinement. Studying partition functions of particles made from D-branes wrapped on algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow trees, we extend the method for computing a refined BPS index, arXiv:0810.4301. For certain D-particles, a finite number of microstates, namely polar states, exclusively realized as bound states, determine an entire partition function (elliptic genus). This underlines their crucial importance: one might call them the `chromosomes' of a D-particle or a black hole. As polar states also can be affected by our refinement, previous predictions on elliptic genera are modified. This can be metaphorically interpreted as `crossing-over in the meiosis of a D-particle'. Our results improve on hep-th/0702012, provide non-trivial evidence for a strong split attractor flow tree conjecture, and thus suggest that we indeed exhaust the BPS spectrum. In the D-brane description of a bound state, the necessity...
Brustein, Ram
2014-01-01
We present a calculation of the rate of information release from a Schwarzschild BH. We have recently extended Hawking's theory of black hole (BH) evaporation to account for quantum fluctuations of the background geometry, as well as for back-reaction and time-dependence effects. Our main result has been a two-point function matrix for the radiation that consists of Hawking's thermal matrix plus off-diagonal corrections that are initially small and become more important as the evaporation proceeds. Here, we show that, if the phases and amplitudes of the radiation matrix are recorded over the lifetime of the BH, then the radiation purifies in a continuous way. We conjecture that our results establish the maximal rate at which information can be released from a semiclassical BH, to be contrasted with the minimal rate that was predicted by Page on the basis of generic unitarity arguments. When the phases of the radiation matrix are not tracked, we show that it purifies only parametrically close to the end of the...
'Black holes': escaping the void.
Waldron, Sharn
2013-02-01
The 'black hole' is a metaphor for a reality in the psyche of many individuals who have experienced complex trauma in infancy and early childhood. The 'black hole' has been created by an absence of the object, the (m)other, so there is no internalized object, no (m)other in the psyche. Rather, there is a 'black hole' where the object should be, but the infant is drawn to it, trapped by it because of an intrinsic, instinctive need for a 'real object', an internalized (m)other. Without this, the infant cannot develop. It is only the presence of a real object that can generate the essential gravity necessary to draw the core of the self that is still in an undeveloped state from deep within the abyss. It is the moving towards a real object, a (m)other, that relativizes the absolute power of the black hole and begins a reformation of its essence within the psyche.
Formation of Supermassive Black Holes
Volonteri, Marta
2010-01-01
Evidence shows that massive black holes reside in most local galaxies. Studies have also established a number of relations between the MBH mass and properties of the host galaxy such as bulge mass and velocity dispersion. These results suggest that central MBHs, while much less massive than the host (~ 0.1%), are linked to the evolution of galactic structure. In hierarchical cosmologies, a single big galaxy today can be traced back to the stage when it was split up in hundreds of smaller components. Did MBH seeds form with the same efficiency in small proto-galaxies, or did their formation had to await the buildup of substantial galaxies with deeper potential wells? I briefly review here some of the physical processes that are conducive to the evolution of the massive black hole population. I will discuss black hole formation processes for `seed' black holes that are likely to place at early cosmic epochs, and possible observational tests of these scenarios.
Black holes and quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Hooft, G. ' t, E-mail: g.thooft@uu.n [Institute for Theoretical Physics, Utrecht University and Spinoza Institute, P.O. Box 80.195, 3508 TD Utrecht (Netherlands)
2010-07-15
After a brief review of quantum black hole physics, it is shown how the dynamical properties of a quantum black hole may be deduced to a large extent from Standard Model Physics, extended to scales near the Planck length, and combined with results from perturbative quantum gravity. Together, these interactions generate a Hilbert space of states on the black hole horizon, which can be investigated, displaying interesting systematics by themselves. To make such approaches more powerful, a study is made of the black hole complementarity principle, from which one may deduce the existence of a hidden form of local conformal invariance. Finally, the question is raised whether the principles underlying Quantum Mechanics are to be sharpened in this domain of physics as well. There are intriguing possibilities.
Singularities Inside Hairy Black Holes
Gal'tsov, D. V.; Donets, E. E.; Zotov, M. Yu.
1997-01-01
We show that the Strong Cosmic Censorship is supported by the behavior of generic solutions on the class of static spherically symmetric black holes in gravitating gauge models and their stringy generalizations.
Singularities Inside Hairy Black Holes
Galtsov, D V; Zotov, M Yu
1998-01-01
We show that the Strong Cosmic Censorship is supported by the behavior of generic solutions on the class of static spherically symmetric black holes in gravitating gauge models and their stringy generalizations.
Black hole accretion disc impacts
Pihajoki, Pauli
2015-01-01
We present an analytic model for computing the luminosity and spectral evolution of flares caused by a supermassive black hole impacting the accretion disc of another supermassive black hole. Our model includes photon diffusion, emission from optically thin regions and relativistic corrections to the observed spectrum and time-scales. We test the observability of the impact scenario with a simulated population of quasars hosting supermassive black hole binaries. The results indicate that for a moderate binary mass ratio of 0.3, and impact distances of 100 primary Schwarzschild radii, the accretion disc impacts can be expected to equal or exceed the host quasar in brightness at observed wavelength {\\lambda} = 510 nm up to z = 0.6. We conclude that accretion disc impacts may function as an independent probe for supermassive black hole binaries. We release the code used for computing the model light curves to the community.
Energy Technology Data Exchange (ETDEWEB)
Darling, D.
1980-10-01
A discussion of Einstein's General Relativity and how it can explain black holes is included. The key idea of general relativity being that gravitational forces are a direct outcome of local curvature of space-time. The more mass something has the deeper the depression or well it causes in space-time. Black holes are supermassive objects, hence their gravity well is so steep even light can't escape. The three properties associated with a black hole are mass angular momentum, and electric charge. Non-rotating, Schwarzchild, and rotating, Kerr, black holes are studied. A Kruskal-Szekeres diagram for each type is given and explained. (SC)
Accretion, primordial black holes and standard cosmology
Indian Academy of Sciences (India)
B Nayak; P Singh
2011-01-01
Primordial black holes evaporate due to Hawking radiation. We find that the evaporation times of primordial black holes increase when accretion of radiation is included. Thus, depending on accretion efficiency, more primordial black holes are existing today, which strengthens the conjecture that the primordial black holes are the proper candidates for dark matter.
Offshell thermodynamic metrics of the Schwarzschild black hole
Wen, Wen-Yu
2016-01-01
Thermodynamic metric usually works only for those black holes with more than one conserved charge, therefore the Schwarzschild black hole was excluded. In this letter, we compute and compare different versions of offshell thermodynamic metric for the Schwarzschild-like black hole by introducing a new degree of freedom. This new degree of freedom could be the running Newton constant, a cutoff scale for regular black hole, a noncommutative deformation, or the deformed parameter in the nonextensive Tsallis-Renyi entropy. The onshell metric of the deformed Schwarzschild solution would correspond to the submanifold by gauge fixing of this additional degree of freedom. In particular, the thermal Ricci scalar for the Schwarzschild black hole, though different for various deformation, could be obtained by switching off the deformation.
Stability of accretion disk around rotating black holes
Mukhopadhyay, B
2004-01-01
I discuss the stability of accretion disks when the black hole is considered to be rotating. I show, how the fluid properties get changed for different choices of angular momentum of black holes. I treat the problem in pseudo-Newtonian approach with a suitable potential from Kerr geometry. When the angular momentum of a black hole is considered to be significant, the valid disk parameter region affects and a disk may become unstable. Also the possibility of shock in an accretion disk around rotating black holes is checked. When the black hole is chosen to be rotating, the sonic locations of the accretion disk get shifted or disappear, making the disk unstable by means of loosing entropy. To bring the disk in a stable situation, the angular momentum of the accreting matter has to be reduced/enhanced (for co/counter-rotating disk) by means of some physical process.
State-space Manifold and Rotating Black Holes
Bellucci, Stefano
2010-01-01
We study a class of fluctuating higher dimensional black hole configurations obtained in string theory/ $M$-theory compactifications. We explore the intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the Hessian of the coarse graining entropy, defined over an ensemble of brane microstates. It has been shown that the state-space geometry spanned by the set of invariant parameters is non-degenerate, regular and has a negative scalar curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes, supersymmetric $AdS_5$ black holes, $D_1$-$D_5$ configurations and the associated BMPV black holes. Interestingly, these solutions demonstrate that the principal components of the state-space metric tensor admit a positive definite form, while the off diagonal components do not. Furthermore, the ratio of diagonal components weakens relatively faster than the off diagonal components, and thus they swiftly come into an equilibrium statistical configuration. Novel aspects of the scali...
Geometric inequalities for black holes
Dain, Sergio
2014-01-01
It is well known that the three parameters that characterize the Kerr black hole (mass, angular momentum and horizon area) satisfy several important inequalities. Remarkably, some of these inequalities remain valid also for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this article recent results in this subject are reviewed.
Magnetic Black Holes Are Also Unstable
Kim, Sang Pyo
2004-01-01
Most black holes are known to be unstable to emitting Hawking radiation (in asymptotically flat spacetime). If the black holes are non-extreme, they have positive temperature and emit thermally. If they are extremal rotating black holes, they still spontaneously emit particles like gravitons and photons. If they are extremal electrically charged black holes, they are unstable to emitting electrons or positrons. The only exception would be extreme magnetically charged black holes if there do not exist any magnetic monopoles for them to emit. However, here we show that even in this case, vacuum polarization causes all magnetic black holes to be unstable to emitting smaller magnetic black holes.
Black hole evaporation within a momentum-dependent metric
Salesi, G
2009-01-01
We investigate the black hole thermodynamics in a "deformed" relativity framework where the energy-momentum dispersion law is Lorentz-violating and the Schwarzchild-like metric is momentum-dependent with a Planckian cut-off. We obtain net deviations of the basic thermodynamical quantities from the Hawking-Bekenstein predictions: actually, the black hole evaporation is expected to quit at a nonzero critical mass value (of the order of the Planck mass), leaving a zero temperature remnant, and avoiding a spacetime singularity. Quite surprisingly, the present semiclassical corrections to black hole temperature, entropy, and heat capacity turn out to be identical to the ones obtained within some quantum approaches.
On the Thermodynamic Geometry of BTZ Black Holes
Sarkar, Tapobrata; Tiwari, Bhupendra Nath; Sarkar, Tapobrata; Sengupta, Gautam; Tiwari, Bhupendra Nath
2006-01-01
We investigate the Ruppeiner geometry of the thermodynamic state space of a general class of BTZ black holes. It is shown that the thermodynamic geometry is flat for both the rotating BTZ and the BTZ Chern Simons black holes in the canonical ensemble. We further investigate the inclusion of thermal fluctuations to the canonical entropy of the BTZ Chern Simons black holes and show that the leading logartithmic correction due to Carlip is reproduced. We establish that the inclusion of thermal fluctuations induces a non zero scalar curvature to the thermodynamic geometry.