The semi-classical derivation of Hawking radiation for axially symmetric, stationary spacetimes with a Killing horizon is examined following the recent quasi-classical tunneling analysis and a simple formula is found for the inverse Hawking temperature $β= 1/T_H$. The formula is invariant under canonical transformations and is shown to be equivalent to the integral of a closed differential 1-form around the horizon enclosing a pole. The Hawking temperature is then given in terms of the winding number in the first homotopy group of the torus formed from the compactified imaginary parts of the analytically continued radial and time variables.
We study the thermodynamics of Gödel-type rotating charged black holes in five-dimensional minimal supergravity. These black holes exhibit some peculiar features such as the presence of closed time-like curves and the absence of globally spatial-like Cauchy surface. We explicitly compute their energies, angular momenta, and electric charges that are consistent with the first law of thermodynamics. Besides, We extend the covariant anomaly cancellation method, as well as the approach of the effective action, to derive their Hawking fluxes. Both the methods of the anomaly cancellation and effecti…
Relations between the tunneling rate and the unified first law of thermodynamics at the apparent horizon of the FRW universe are investigated. The tunneling rate arises as a consequence of the unified first law of thermodynamics in such a dynamical system. The analysis shows obviously how the tunneling is intimately connected with the unified first law of thermodynamics through the principle of conservation of energy.
We show that the first law of the black hole thermodynamics can lead to the tunneling probability through the quantum horizon by calculating the change of entropy with the quantum gravity correction and the change of surface gravity is presented clearly in the calculation. The method is also applicable to the general situation which is independent on the form of black hole entropy and this verifies the connection of black hole tunneling with thermodynamics further. In the end we discuss the crucial role of the relation between the radiation temperature and surface gravity in this derivation.
We construct a new exact solution in the 5D Einstein-Maxwell-dilaton gravity describing a magnetized squashed black hole. We calculate its physical characteristics, and derive the Smarr-like relations. The Hawking radiation of the solution is also investigated by calculating the greybody factor for the emission of massless scalar particles in the low-energy regime. In distinction to the case of asymptotically flat magnetized black holes, the thermodynamical characteristics and the Hawking radiation of the solution depend on the external magnetic field, and consequently can be tuned by its vari…
String theory usually represents quantum black holes as systems whose statistical mechanics reproduces Hawking's thermodynamics in a very satisfactory way. Complicated brane theoretical models are worked out, as quantum versions of Supergravity solutions. These models are then assumed to be in thermal equilibrium: this is a little cheating, because one is looking for an explanation of the seeming thermodynamical nature of black holes, so they cannot be {\it assumed} to be finite temperature systems! In the model presented here, the black body spectrum arises with no statistical hypothesis as a…
An analysis of relations between the tunneling rate and the unified first law of thermodynamics at the trapping horizons of two kinds of spherically symmetric dynamical black holes is investigated. The first kind is the Vaidya-Bardeen black hole, the tunneling rate $Γ\sim e^{\triangle S}$ can be obtained naturally from the unified first law at the apparent horizon, which holds the form $dE_{H}=TdS+WdV$. Another is the McVittie solution, the action of the radial null geodesic of the outgoing particles does not always has a pole at the apparent horizon, while the ingoing mode always has one. The…
In this paper, we investigate the thermodynamics especially the Hawking-Page-like phase transition of the McVittie space-time. We formulate the first law of thermodynamics for the McVittie black hole, and find that the work density $W$ of the perfect fluid plays the role of the thermodynamic pressure, i.e. $P$:=$-W$. We also construct the thermodynamic equation of state for the McVittie black hole. Most importantly, by analysing the Gibbs free energy, we find that the Hawking-Page-like phase transition from FRW spacetime to McVittie black hole is possible in the case $P>0$.
An inexhaustive review of Hawking radiation and black hole thermodynamics is given, focusing especially upon some of the historical aspects as seen from the biased viewpoint of a minor player in the field on and off for the past thirty years.
We investigate the thermodynamic curvature in the Hawking-Page phase transition and the second-order phase transition of the AdS black hole. It is shown that the thermodynamic curvature has the same behavior in these two different phase transitions. Specifically, the thermodynamic curvature in the Hawking-Page phase transition is the power function of the Hawking-Page phase transition temperature with exponent related to the spacetime dimension, or is invariably proportional to the reciprocal of the Hawking-Page phase transition entropy. For the thermodynamic curvature in the second-order phas…
Thermodynamic properties of a class of black $p$-branes in $D$-dimensions considered by Duff and Lu are investigated semi-classically. For black $(d-1)$-brane, thermodynamic quantities depend on $D$ and $d$ only through the combination $\tilde d \equiv D-d-2$. The behavior of the Hawking temperature and the lifetime vary with $\tilde d$, with a critical value $\tilde d=2$. For $\tilde d>2$, there remains a remnant, in which non-zero entropy is stored. Implications of the fact that the Bekenstein-Hawking entropy of the black $(d-1)$-brane depend only on $\tilde d=D-d-2$ is discussed from the po…
In this paper, we start with black brane and construct specific space-time which violates hyperscaling. In order to obtain the string solution we apply Null-Melvin-Twist and $KK$-reduction. By using the difference action method we study thermodynamics of system to obtain Hawking-Page phase transition. In order to have hyperscaling violation we need to consider $θ=\frac{d}{2}.$ In that case the free energy $F$ is always negative and our solution is thermal radiation without a black hole. Therefore we find that there is not any Hawking-Page transition. Also, we discuss the stability of system an…
We present a derivation of Hawking radiation through tunneling mechanism for a general class of asymptotically flat, spherically symmetric spacetimes. The tunneling rate $Γ\sim \exp{(ΔS)}$ arises as a consequence of the first law of thermodynamics, TdS=dE + PdV. Therefore, this approach demonstrates how tunneling is intimately connected with the first law of thermodynamics through the principle of conservation of energy. The analysis is also generally applicable to any reasonable theory of gravity so long as the first law of thermodynamics for horizons holds in the form, TdS=dE + PdV.
An analogy between the subtraction procedure in the Gibbons-Hawking Euclidean path integral approach to Horizon's Thermodynamics and the Casimir effect is shown. Then a conjecture about a possible Casimir nature of the Gibbons-Hawking subtraction is made in the framework of Sakharov's induced gravity. In this framework it appears that the degrees of freedom involved in the Bekenstein-Hawking entropy are naturally identified with zero--point modes of the matter fields. Some consequences of this view are sketched.
We consider the BTZ black hole surrounded by the conformal scalar field. Within general relativity, the resonant \emph{quasinormal} (QN) modes dominate in the response of a black hole to external perturbations. At the same time, the metric of an evaporating black hole is affected by the Hawking radiation. We estimate the shift in the quasinormal spectrum of the BTZ black hole stipulated by the back reaction of the Hawking radiation. For the case of the 2+1 dimensional black hole the corrected (by $\sim \hbar$) metric is an \emph{exact} solution [C.Martines, J.Zanelli (1997)]. In addition, in t…
A black hole can be regarded as a thermodynamic system described by a grand canonical ensemble. In this paper, we study the Bekenstein-Hawking entropy of higher-dimensional rotating black holes using the Euclidean path-integral method of Gibbons and Hawking. We give a general proof demonstrating that ignoring quantum corrections, the Bekenstein-Hawking entropy is equal to one-fourth of its horizon area for general higher-dimensional rotating black holes.
We investigate the thermodynamic properties of the Hawking-Page phase transition of AdS black holes. We present evidence for the existence of two universal critical constants associated with the Hawking-Page (HP) and minimum black hole thermodynamical transition points. These constants are defined by C_S =\frac{S_{HP}-S_{min}}{S_{min}} and C_T =\frac{T_{HP}-T_{min}}{T_{min}} where S_{min}(S_{HP}) and T_{min}(T_{HP}) are the minimal (HP phase transition) entropy and temperature, respectively, below which no black hole can exist. For a large class of four dimensional non-rotating black holes, we…
he quasi-classical method of deriving Hawking radiation is investigated. In order to recover the original Hawking temperature one must take into account a previously ignored contribution coming from the temporal part of the action. This contribution plus a contribution coming from the spatial part of the action gives the correct temperature.
In the context of black hole chemistry, we study the thermodynamics of asymptotically de Sitter black holes with conformal scalar hair in Einstein gravity. The hair parameter allows us to attain thermodynamic equilibrium between the event horizon and the cosmological horizon. We find that the system of the black hole and the de Sitter space surrounding it undergo a Reverse Hawking-Page phase transition provided we consider the grand-canonical ensemble.
Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, …
We investigate the nonequilibrium back reaction on the Schwarzschild black hole from the radiation field. The back reactions are characterized by the membrane close to the black hole. When the membrane is thin, we found that larger temperature difference can lead to more significant negative surface tension, larger thermodynamic dissipation cost and back reaction in energy and entropy as well as larger black hole area. This may be relevant to the primordial black holes in early universe. Moreover, our nonequilibrium model can resolve the inconsistency issue of the black hole back reaction unde…
In the spherically symmetric case the Einstein field equations take on their simplest form for a matter-density rho = 1 / (8 pi r^2), from which a radial metric coefficient g_{rr} \propto r follows. The boundary of an object with such an interior matter-density is situated slightly outside of its gravitational radius. Its surface-redshift scales with z \propto \sqrt{r}, so that any such large object is practically indistinguishable from a black hole, as seen from exterior space-time. The interior matter has a well defined temperature, T \propto 1 / \sqrt{r}. Under the assumption, that the inte…
Recently, exotic black holes whose masses and angular momenta are interchanged have been found, and it is known that their entropies depend only on the $inner$ horizon areas. But a basic problem of these entropies is that the second law of thermodynamics is not guaranteed, in contrast to the Bekenstein-Hawking entropy. Here, I find that there is another entropy formula which recovers the usual Bekenstein-Hawking form, but the characteristic angular velocity and temperature are identified with those of the inner horizon, in order to satisfy the first law of black hole thermodynamics. The temper…
I give a fairly systematic and thorough presentation of the case for regarding black holes as thermodynamic systems in the fullest sense, aimed at students and non-specialists and not presuming advanced knowledge of quantum gravity. I pay particular attention to (i) the availability in classical black hole thermodynamics of a well-defined notion of adiabatic intervention; (ii) the power of the membrane paradigm to make black hole thermodynamics precise and to extend it to local-equilibrium contexts; (iii) the central role of Hawking radiation in permitting black holes to be in thermal contact …
We consider a Schwarzschild black hole immersed in a ghost condensate background. It is shown that the Hawking radiation in the quanta of small perturbations around this background is highly suppressed- in particular it is not given by a thermal spectrum. This result is in accord with observations that such black holes can be used to violate the generalized second law of thermodynamics, and thus cannot have a standard entropy/area relation.
This work explores the role of thermodynamic fluctuations in the two parameter Hawking radiating black hole configurations. The system is characterized by an ensemble of arbitrary mass and radiation frequency of the black holes. In the due course of the Hawking radiations, we find that the intrinsic geometric description exhibits an intriguing set of exact pair correction functions and global correlation lengths. We investigate the nature of the constant amplitude radiation and find that it's not stable under fluctuations of the mass and frequency. Subsequently, the consideration of the York m…
Probing the thermodynamic properties of the Hawking-Page phase transition of asymptotically-flat black holes in Rényi statistics. We reveal the evidence for the persisting of the dual universal formula associated with the Hawking-Page (HP) and minimum black hole thermodynamical transition points. Our study unveils the universal properties of the black holes in different statistics, in particular beyond the Gibbs-Boltzmann formalism, and motivates a further promising bridge between the nonextensivity Rényi parameter λ and the cosmological constant ? . Besides, we discover that universal ratios …
The tunneling formalism in the Hamilton-Jacobi approach is adopted to study Hawking radiation of massless Dirac particles from spherically symmetric black hole spacetimes incorporating the effects of the generalized uncertainty principle. The Hawking temperature is found to contain corrections from the generalized uncertainty principle. Further, we show from this result that the ratio of the GUP corrected energy of the particle to the GUP corrected Hawking temperature is equal to the ratio of the corresponding uncorrected quantities. This result is then exploited to compute the Hawking tempera…
We present exact analytical black hole solutions with conformal anomaly in AdS space and discuss the thermodynamical properties of these black hole solutions. These black holes can have a positive, zero and negative constant curvature horizon, respectively. For the black hole with a positive constant curvature horizon, there exists a minimal horizon determined by the coefficient of the trace anomaly, the black hole with a smaller horizon is thermodynamically unstable, while it is stable for the case with a larger horizon. The Hawking-Page transition happens in this case. For the black hole wit…
To explore the mechanism for the entropic force proposal in Entropic Gravity, we propose a specific thermodynamic process for states thermalized in local Hawking Temperature. We find when Casini's version of the Bekenstein bound is saturated, the thermodynamic force derived in the entanglement first law matches the local inertial force for the Schwarzschild solution, except for a negligible statistics-dependent factor. We argue the gravity viewed by static observers may have observable effects emerged from quantum statistics. The successful detailed calculation in this simple model inspires an…
We argue that, when working with the appropriate set of thermodynamical variables, the Bekenstein-Hawking law still holds for asymptotically flat black objects with conical singularities. The mass-energy which enters the first law of thermodynamics does not, however, coincide with the ADM mass; it differs from the latter by the energy associated with the conical singularity, as seen by an asymptotic, static observer. These statements are supported by a number of examples: the Bach-Weyl (double-Schwarzschild) solution, its dihole generalisation in Einstein-Maxwell theory and the five dimensiona…
In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase tra…
In this paper we investigate an exact spectrum of quasi normal modes (QNMs) for perturbations of a scalar field coupled non-minimally with the Einstein tensor of an uncharged, non-rotating Banados, Teitelboim, and Zanelli (BTZ) black hole in three-dimensional spacetime. Due to the geometry around the black hole, the scalar field encounters an effective potential barrier. We study this potential numerically and derive exact numerical results for the greybody factors (GFs) and discuss their profiles in terms of the coupling constant and black hole parameters. We then proceed to derive the Hawkin…
We consider quasinormal modes and Hawking radiation of four-dimensional asymptotically flat black holes in the most general up to-cubic-order-in-curvature dimension-independent Einsteinian theory of gravity that shares its graviton spectrum with the Einstein theory on constant curvature backgrounds. We show that damping rate and real oscillation frequencies of quasinormal modes for scalar, electromagnetic and Dirac fields are suppressed once the coupling with the cubic term is on. The intensity of Hawking radiation is suppressed as well, leading to, roughly, one order longer lifetime at a suff…
The persistence of a suitable notion of black hole thermodynamics in Lorentz breaking theories of gravity is not only a non-trivial consistency test for such theories, it is also an interesting investigation {\em per se}, as it might help us identifying the crucial features at the root of these surprising laws governing such purely gravitational objects. In past investigations, controversial findings were presented in this sense. With the aim of settling this issue, we present here two complementary derivations of Hawking radiation in geometries endowed with universal horizons: a novel feature…
We investigate the thermodynamics of a general class of exact 4-dimensional asymptotically Anti-de Sitter hairy black hole solutions and show that, for a fixed temperature, there are small and large hairy black holes similar to the Schwarzschild-AdS black hole. The large black holes have positive specific heat and so they can be in equilibrium with a thermal bath of radiation at the Hawking temperature. The relevant thermodynamic quantities are computed by using the Hamiltonian formalism and counterterm method. We explicitly show that there are first order phase transitions similar to the Hawk…
We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=\frac{\cal K}{2π}$ connecting the black hole temperature ($T_h$) with the surface gravity ($\cal K$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed for…
Thermodynamics of the BTZ black hole in noncommutative geometry is studied. We work out the Hawking temperature and entropy which reduce to their commutative limits when the noncommutativity parameter tends to zero. We also discuss the range of validity of the Hawking area law in the noncommutative case and provide graphical analysis. We see that the law is not valid unless the outer horizon is very large.
In this paper, we investigate the thermodynamic properties of the RN-AdS black hole with cloud of strings and quintessence in rainbow gravity with the stationary (ST) orthonormal frame and the free-fall (FF) orthonormal frame. After the SF and the FF rainbow metric is obtained, we get the Hawking temperature and the entropy, and their physical meanings are discussed. We find that, for the ST rainbow RN-AdS black hole with cloud of strings and quintessence, the effect of rainbow gravity is to increase the Hawking temperature but decrease the entropy of the black hole. However, for the FF rainbo…
We investigate the scalar field system over a charged Weyl black hole, depicted by a parameter $λ$. It is found that the imaginary part of the quasinormal mode spectra is always negative and the perturbation does not increase with the time, indicating that the system is stable under scalar field perturbation. Furthermore, the quasinormal mode spectra and Hawking radiation exhibit a qualitatively similar characteristic in that they both rise with rising $λ$ and approach a constant when $λ$ is large enough. Especially, we would like to emphasize that an exponential decay obviously emerges in the…
The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there is an intense activity to understand thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment is related to the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black-holes --- that are simple yet m…
We show that the Hawking--Bekenstein entropy formula is modified by a factor of $8/3$ if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition $ε=Mc^2/V$, which is the average energy density of the Hawking radiation. This volume scales as $V \sim M^5$, agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state $S(E,V)\sim E^{3/4}V^{1/4}$. The…
The non-strictly continuous character of the Hawking radiation spectrum generates a natural correspondence between Hawking radiation and black hole (BH) quasi-normal modes (QNM). In this work, we generalize recent results on this important issue to the framework of Kerr BHs (KBH). We show that also for the KBH, QNMs can be naturally interpreted in terms of quantum levels. Thus, the emission or absorption of a particle is in turn interpreted in terms of a transition between two different levels. At the end of the paper, we also generalize some concepts concerning the "effective state" of a KBH.
Recently Gibbons {\it et al.} in hep-th/0408217 defined a set of conserved quantities for Kerr-AdS black holes with the maximal number of rotation parameters in arbitrary dimension. This set of conserved quantities is defined with respect to a frame which is non-rotating at infinity. On the other hand, there is another set of conserved quantities for Kerr-AdS black holes, defined by Hawking {\it et al.} in hep-th/9811056, which is measured relative to a frame rotating at infinity. Gibbons {\it et al.} explicitly showed that the quantities defined by them satisfy the first law of black hole the…
The seminal works of Bekenstein and Hawking have revealed that black holes have a well-defined thermodynamic description. In particular, it is often stated in the physical literature that black holes, like mundane physical systems, obey the first law of thermodynamics: $ΔS=ΔE/T_{\text{BH}}$, where $T_{\text{BH}}$ is the Bekenstein-Hawking temperature of the black hole. In the present work we test the regime of validity of the thermodynamic description of gravity. In particular, we provide compelling evidence that, due to quantum effects, the first law of thermodynamics breaks down in the low-t…
Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a $9\%$ decrease in the damping rate and up to a $6\%$ decrease in the real oscillation frequency. However, the intensity of Hawking ra…
The Rényi and Tsallis entropies are discussed as possible alternatives to the Bekenstein-Hawking area-law entropy. It is pointed out how replacing the entropy notion, but not the Hawking temperature and the thermodynamical energy may render the whole black hole thermodynamics inconsistent. The possibility to relate the Rényi and Tsallis entropies with the quantum gravity corrected Bekenstein-Hawking entropy is discussed.
The rotating linear dilatonic black hole is an asymptotically non-flat solution to Einstein-Maxwell-Dilaton-Axion gravity theory due to the existence of non-trivial matter fields. We have analytically studied the wave equation of scalar field in this background and shown that the radial wave equation can be solved in terms of hypergeometric function. By determining the ingoing and the outgoing fluxes at the asymptotic infinity, we have found the analytical expressions for reflection coefficient and greybody factor for certain scalar modes. In the high frequency regime, we obtain the Hawking te…
The present thesis attempts to study the effect of scalar fields on Hawking radiation and quasinormal modes of black holes. We selected a static, spherically symmetric electrically charged black hole with an additional scalar 'hair' for our analysis. The scalar 'hair' is sourced by a scalar field, conformally coupled to the Einstein-Hilbert action. The scalar field can survive even in the absence of the black hole's electric charge and is characterized as a 'primary hair'. This scalar field changes the gravitational constant, and hence modifies the ADM (Arnowitt-Deser-Missner) mass of the blac…
The present equilibrium formulation of thermodynamics for black holes has several drawbacks, such as assuming the same temperature for black hole and heat bath. Recently the author formulated non-equilibrium thermodynamics for glassy systems. This approach is applied to black holes, with the cosmic background temperature being the bath temperature, and the Hawking temperature the internal temperature. Both Hawking evaporation and absorption of background radiation are taken into account. It is argued that black holes did not form in the very early universe.
