We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasi-local gravitational energy found recently for $f(R)$ gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the FRW spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for $f(R)$ gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.
Universal thermodynamics for FRW model of the Universe bounded by apparent/event horizon has been considered for massive gravity theory. Assuming Hawking temperature and using the unified first law of thermodynamics on the horizon, modified entropy on the horizon has been determined. For simple perfect fluid with constant equation of state, generalized second law of thermodynamics and thermodynamical equilibrium have been examined on both the horizons.
In this article we have used the recently introduced redefined Hawking temperature on the event horizon and investigated whether the generalised second law of thermodynamics (GSLT) and thermodynamic equilibrium holds for both the event and the apparent horizons. Here we have considered FRW universe and examined the GSLT and thermodynamic equilibrium with three examples. Finally, we have concluded that from the thermodynamic viewpoint, the universe bounded by the event horizon is more realistic than that by the apparent horizon at least for some examples.
The paper deals with universal thermodynamics for FRW model of the universe bounded by apparent (or event) horizon. Assuming Hawking temperature on the horizon, the unified first law is examined on the horizon for different gravity theories. The results show that equilibrium configuration is preserved with a modification to Bekenstein entropy on the horizon.
The thermodynamic properties of Cauchy horizon is a matter of interest. Event horizon and Cauchy horizon together can enlighten us about the micro-states of a black hole. In addition, if we consider a black hole metric modified with quantum terms, which is not forcing the geodesics to focus at a singularity, the study of horizons becomes much more interesting. The spacelike behavior inside the Cauchy horizon has a deep impact on the related thermodynamics. We analyze different thermodynamic product to check whether a right left string theory mode's addition type representation for the concerne…
In this brief communication, we have studied the validity of the first law of thermodynamics for the universe bounded by event horizon with two examples. The key point is the appropriate choice of the temperature on the event horizon. Finally, we have concluded that universe bounded by the event horizon may be a Bekenstein system and the Einstein's equations and the first law of thermodynamics on the event horizons are equivalent.
In an accelerated expanding universe, one can expect the existence of an event horizon. It may be interesting to study the thermodynamics of the Friedmann-Robertson-Walker (FRW) universe at the event horizon. Considering the usual Hawking temperature, the first law of thermodynamics does not hold on the event horizon. To satisfy the first law of thermodynamics, it is necessary to redefine Hawking temperature. In this paper, using the redefinition of Hawking temperature and applying the first law of thermodynamics on the event horizon, the Friedmann equations are obtained in f(R) gravity from t…
It is shown that the differential form of Friedmann equations of FRW universe can be recast as a similar form of the first law, $T_{h}dS_{h} = dE + WdV$, of thermodynamics at the apparent horizon of FRW universe filled with the viscous fluid. It is also shown that the generalized second law of thermodynamics holds at the apparent horizon of FRW universe and preserves dominant energy condition.
By regarding the Einstein equations as equation(s) of state, we demonstrate that a full cohomogeneity horizon first law can be derived in horizon thermodynamics. In this approach both the entropy and the free energy are derived concepts, while the standard (degenerate) horizon first law is recovered by a Legendre projection from the more general one we derive. These results readily generalize to higher curvature gravities and establish a way of how to formulate consistent black hole thermodynamics without conserved charges.
To investigate the relationship between gravity and thermodynamics in the case of dynamic systems, we interpret the apparent horizon of the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime as a thermodynamic system. We derive the corresponding fundamental equation in the entropy representation and explore the consequences of demanding the fulfillment of the classical laws of thermodynamics. We investigate in detail the case of an FLRW spacetime with and without cosmological constant. We show that the interpretation of the apparent horizon as a thermodynamic system is possible only under ce…
We study the irreversible (non-equilibrium) thermodynamics of FRW universe containing only dark energy. Using the modified entropy-area relation which is motivated from the loop quantum gravity, we calculate the entropy-corrected form of the apparent horizon of FRW universe.
The present work deals with a detailed study of universal thermodynamics in different modified gravity theories. The validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe bounded by a horizon (apparent/event) in f(R)-gravity, Einstein-Gauss-Bonnet gravity, RS-II brane scenario and DGP brane model has been investigated. In the perspective of recent observational evidences, the matter in the Universe is chosen as interacting holographic dark energy model. The entropy on the horizons are evaluated from the validity of the unified firs…
We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all kinematical parameters of nonstationary radiating black holes in terms of null vectors, we demonstrate that it is possible to interpret the Einstein field equations near the apparent horizon in the form of a thermodynamical identity $TdS=dE+PdV$.
The comment arXiv:1204.2729v1 is completely wrong. The author makes serious mistakes in calculations and judgement. The errors are made at the level of basic undergraduate statistical mechanics.
Certain dynamical black hole solutions can be mapped to static spacetimes by conformal metric transformations. This mapping provides a physical link between the conformal Killing horizon of the dynamical black hole and a Killing horizon of the static spacetime. We show how this conformal relation can be used to derive thermodynamic properties for the dynamical black holes. Although these horizons are defined quasi-locally and can be located by local experiments, they are distinct from other popular notions of quasi-local horizons such as apparent horizons. Thus in the dynamical Vaidya spacetim…
The modified first laws of thermodynamics at the black hole horizon and the cosmological horizon of the Schwarzschild de Sitter black hole and the apparent horizon of the Friedmann-Robertson-Walker cosmology are derived by the surface tensions, respectively. The corresponding Smarr relations are obeyed. For the black hole, the cosmological constant is first treated as a fixed constant, and then as a variable associated to the pressure. The law at the apparent horizon takes the same form as that at the cosmological horizon, but is different from that at the black hole horizon. The positive temp…
As is already known, a spacetime horizon acts like a boundary of a thermal system an we can associate with it notions as temperature and entropy. Following the work of M. Akbar, in this paper we will show how it is possible to interpret the field equation of a charged BTZ black hole near horizon as a thermodynamic identity dE=TdS+PdA+PhidQ, where Phi is the electric potential and Q is the electric charge of BTZ black hole. These results indicate that the field equations for the charged BTZ black hole possess intrinsic thermodynamic properties near horizon.
The work deals with the thermodynamics of the universe bounded by the event horizon. The matter in the universe has three constituents namely dark energy, dark matter and radiation in nature and interaction between then is assumed. The variation of entropy of the surface of the horizon is obtained from unified first law while matter entropy variation is calculated from the Gibbss' law. Finally, validity of the generalized second law of thermodynamics is examined and conclusions are written point wise.
Our aim is to investigate the thermodynamic properties of the universe bounded by the cosmological event horizon and dominated by the tachyon fluid. We give two different laws of evolution of our universe. Further, we show the first law and the generalized second law of thermodynamics (GSLT) are both satisfied in two cases, but their properties of the thermodynamic equilibrium are totally different. Besides, under our solutions, we find the validity of the laws of thermodynamics is irrelevant with the parameters of the tachyon fluid. Finally, we conclude that the universe bounded by the cosmol…
In the context of modified $f(R)$ gravity theory, we study time-dependent wormhole spacetimes in the radiation background. In this framework, we attempt to generalize the thermodynamic properties of time-dependent wormholes in $f(R)$ gravity. Finally, at event horizon, the rate of change of total entropy has been discussed.
Based on a recent proposal for the volume inside a black hole, we calculate the entropy associated with this volume and show that such entropy is proportional to the surface area of the black hole. Together with the consideration of black hole radiation, we find that the thermodynamics associated with the entropy is likely to be caused by the vacuum polarization near the horizon.
On the basis of horizon thermodynamics we study the thermodynamic stability of black holes constructed in general relativity and Gauss-Bonnet gravity. In the framework of horizon thermodynamics there are only five thermodynamic variables $E,P,V,T,S$. It is not necessary to consider concrete matter fields, which may contribute to the pressure of black hole thermodynamic system. In non-vacuum cases, we can derive the equation of state, $P=P(V,T)$. According to the requirements of stable equilibrium in conventional thermodynamics, we start from these thermodynamic variables to calculate the heat …
In this paper, we study different cases of the charged rotating BTZ black hole with reference to their horizons. For the existence of these cases conditions on mass, charge and angular momentum of the black hole are obtained. It is also shown that the Einstein field equations for the charged rotating BTZ black hole at the horizon can be expressed as first law of thermodynamics, $dE=TdS+ΩdJ+Φdq+P_{r}dA$.
We investigate the validity of the generalized second law in irreversible thermodynamics in a non-flat FRW universe containing the interacting dark energy with cold dark matter. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. We show that for the present time, the generalized second law in nonequilibrium thermodynamics is satisfied for the special range of the energy transfer constants.
Entanglement entropy is often speculated as a strong candidate for the origin of the black-hole entropy. To judge whether this speculation is true or not, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of the black hole entropy. It is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a `thermodynamics of entanglement' by introduc…
We derive black hole entropy based on the near-horizon symmetries of black hole space-times. To derive these symmetries we make use of an $(R,T)$-plane close to a Killing horizon. We identify a set of vector fields that preserves this plane and forms a Witt algebra. The corresponding algebra of Hamiltonians is shown to have a non-trivial central extension. Using the Cardy formula and the central charge we obtain the Bekenstein-Hawking entropy.
We show, by using Regge calculus, that the entropy of any finite part of a Rindler horizon is, in the semi-classical limit, one quarter of the area of that part. We argue that this result implies that the entropy associated with any horizon of spacetime is, in semi-classical limit, one quarter of its area. As an example, we derive the Bekenstein-Hawking entropy law for the Schwarzschild black hole.
We explicitly prove the horizon-entropy increase law for both causal and quasi-locally defined horizons in scalar-tensor and $f(R)$ gravity theories. Contrary to causal event horizons, future outer trapping horizons are not conformally invariant and we provide a modification of trapping horizons to complete the proof, using the idea of generalised entropy. This modification means they are no longer foliated by marginally outer trapped surfaces but fixes the location of the horizon under a conformal transformation. We also discuss the behaviour of horizons in "veiled" general relativity and sho…
Here we consider our universe as inhomogeneous spherically symmetric Lemaitre-Tolman-Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.
Thermodynamics on the cosmological apparent horizon of a flat Friedmann-Lemaitre-Robertson-Walker metric has been investigated with Bekenstein entropy and Hawking temperature on the horizon, and Unruh temperature for the fluid inside the horizon. This temperature is experienced by a radial comoving observer infinitesimally close to the horizon due to the pressure exerted by the fluid bounded by the horizon. An expression for the entropy of the fluid has been obtained which is found to be proportional to the volume of the thermodynamic system which implies that the Unruh temperature of the flui…
In blackhole physics, the second law of thermodynamics is generally valid whether the blackhole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of blackhole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics(GSLT). Here, we have assumed the universe to be bounded by the event-horizon or filled with perfect fluid and holographic dark energy in two cases. Thus considering entropy to be an arbitrary function of the area of the event-horizon, we have t…
We discuss how to define a kinematical horizon entropy on a causal set. We extend a recent definition of horizon molecules to a setting with a null hypersurface crossing the horizon. We argue that, as opposed to the spacelike case, this extension fails to yield an entropy local to the hypersurface-horizon intersection in the continuum limit when the causal set approximates a curved spacetime. We then investigate the entropy defined via the Spacetime Mutual Information between two regions of a causal diamond truncated by a causal horizon, and find it does limit to the area of the intersection.
In this paper, we extend the calculation of the entropy of the nonrotating isolated horizons in 4 dimensional spacetime to that in a higher dimensional spacetime. We show that the boundary degrees of freedom on an isolated horizon can be described effectively by a punctured $SO(1,1)$ BF theory. Then the entropy of the nonrotating isolated horizon can be calculated out by counting the microstates. It satisfies the Bekenstein-Hawking law.
In this paper we show that the gravitational field equations of $(n+1)$% -dimensional topological black holes with constant horizon curvature, in cubic and quartic quasi-topological gravity, can be recast in the form of the first law of thermodynamics, $dE=TdS-PdV$, at the black hole horizon. This procedure leads to extract an expression for the horizon entropy as well as the energy (mass) in terms of the horizon radius, which coincide exactly with those obtained in quasi-topological gravity by solving the field equations and using the Wald's method. We also argue that this approach is powerfu…
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In the first part of the paper, a general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced which makes it possible, firstly, to judge special assumptions for the entropy density 4-vector made by other authors with respect to their generality and validity and, secondly, to determine entropy supply and e…
This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an extensive quantity and can be well-defined. To show this, we make a comparison with a classical ideal gas system whose statistical description makes only sense if an additional 1/N!-factor is included in the state counting in order to cure the Gibbs paradox. The case of the statistical description of a quantum isolated horizon is elaborated, to make the cla…
We discuss the thermodynamic limit in the canonical area ensemble used in loop quantum gravity to model quantum black holes. The computation of the thermodynamic limit is the rigorous way to obtain a smooth entropy from the counting entropy given by a direct determination of the number of microstates compatible with macroscopic quantities (the energy in standard statistical mechanics or the area in the framework presented here). As we will show in specific examples the leading behavior of the smoothed entropy for large horizon areas is the same as the counting entropy but the subleading contri…
Verification of the First Law of Horizon Thermodynamics for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman Black Holes in Four-Dimensional f(R) Gravity with Dual Scalar Fields
We investigate the thermodynamic arrow of time in a time-symmetrically recollapsing universe by calculating quantum mechanically the entropy production of a massive scalar field. It is found that even though the Hamiltonian has a time-reversal symmetry with respect to the maximum expansion of the universe, the entropy production is generic and the total entropy of the scalar field increases monotonically. We conclude that the thermodynamic arrow of time is a universal phenomenon even in the expanding and subsequently recollapsing universe due to the parametric interaction of matter field with …
In the context of the teleparallel equivalent of general relativity the concept of gravitational pressure and gravitational energy-momentum arisen in a natural way. In the case of a Friedmann-Lemaitre-Robertson-Walker space FLRW we obtain the total energy contained inside the apparent horizon and the radial pressure over the apparent horizon area. We use these definitions to written a thermodynamics relation $T_{A}dS_{A} = dE_{A}+P_{A}dV_{A}$ at the apparent horizon, where $E_{A}$ is the total energy inside the apparent horizon, $V_{A}$ is the areal volume of the apparent horizon, $P_{A}$ is t…
We calculate the exact degeneracy of states corresponding to the area operator in the framework of semiclassical loop quantum gravity, using techniques of combinatorial theory. The degeneracy counting is used to find entropy of apparent horizons derived from generalised coherent states which include a sum over graphs. The correction to the entropy is determined as exponentially decreasing in area.
We test on the 2+1 dimensional black hole the quantization method that we have previously proposed in four dimensions. While in the latter case the horizon dynamics is described, at the effective level, by the action of a relativistic membrane, in the 2+1 case it is described by a string. We show that this approach reproduces the correct value of the temperature and entropy of the 2+1 dimensional black hole, and we write down the Schroedinger equation satisfied by the horizon wave function.
This work is to study the generalized second law (GSL) of thermodynamics in tachyon cosmology where the boundary of the universe is assumed to be enclosed by a dynamical apparent horizon. The model is constrained with the observational data. The two logarithmic and power law corrected entropy is also discussed and conditions to validate the GSL and corrected entropies are obtained.
We show that there are implications on thermodynamics that come from the existence of the initial cosmic singularity. At present time this is more a conceptual change than an observable one. However at very early cosmic times there is a big difference between the actual behavior of thermodynamic quantities and the behavior assumed in the standard cosmological model. We present the discussion of two systems: an ideal monatomic gas at present, and a photon gas at the early Universe. We show the striking result that the entropy density goes to zero as the cosmic time goes to zero. This in turn, p…
The first law of black hole thermodynamics can be read off from the field equations at the horizon. Until now, for black holes with multiple horizons the field equations only at the outer horizon were employed with a particular constraint. In this paper, however, we suggest that for a black hole with multiple horizons the field equations at the inner horizon as well as the outer horizon should be needed in order to obtain the first law of black hole thermodynamics in general.
Recent observational evidences claim an accelerating expansion of the universe at present epoch. It is commonly incorporated in standard cosmology by the introduction of an exotic matter (that violates the strong energy condition) known as dark energy (DE). As event horizon exists for accelerating universe so there has been a lot of work on universal thermodynamics (i.e., thermodynamics of the universe bounded by apparent or event horizon). Recently, thermodynamical equilibrium has been examined for both the horizons. In the present work we show that universal thermodynamics with event horizon…
We propose a dual thermodynamic description of a classical instability of generalised black hole spacetimes. From a thermodynamic perspective, the instability is due to negative compressibility in regions where the Casimir pressure is large. The argument indicates how the correspondence between thermodynamic and classical instability for horizons may be extended to cases without translational invariance.
It is well known that, for a wide class of spacetimes with horizons, Einstein equations near the horizon can be written as a thermodynamic identity. It is also known that the Einstein tensor acquires a highly symmetric form near static, as well as stationary, horizons. We show that, for generic static spacetimes, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity. We further extend this result to generic static spacetimes in Lanczos-Lovelock gravity, and show that the near…
When black holes are dynamical, event horizons are replaced by apparent and trapping horizons. Conformal and Kerr-Schild transformations are widely used in relation with dynamical black holes and we study the behaviour under such transformations of quantities related to the thermodynamics of these horizons, such as the Misner-Sharp-Hernandez mass (internal energy), the Kodama vector, surface gravity, and temperature. The transformation properties are not those expected on the basis of naive arguments.
There exist several well-established procedures for computing thermodynamics for a single horizon spacetime. However, for a spacetime with multi-horizon, the thermodynamics is not very clear. It is not fully understood whether there exists a global temperature for the multi-horizon spacetime or not. Here we show that a global temperature can exist for Schwarzschild-de Sitter spacetime, Reissner-Nordstrom-de Sitter spacetime, and rotating BTZ black hole. This temperature does not coincide with the conventional Hawking temperature related to the outer horizon. We also show that the total entropy…
We propose an expression for the entropy density associated with the Local Causal Horizons in any diffeomorphism invariant theory of gravity. If the black-hole entropy of the theory satisfies the physical process version of the first law of thermodynamics then our proposed entropy satisfies the Clausius relation. Thus, our study shows that the thermodynamic nature of the spacetime horizons is not restricted to the black holes; it also applies to the local causal horizons in the neighborhood of any point in the spacetime.
The comparison of geometrical properties of black holes with classical thermodynamic variables reveals surprising parallels between the laws of black hole mechanics and the laws of thermodynamics. Since Hawking's discovery that black holes when coupled to quantum matter fields emit radiation at a temperature proportional to their surface gravity, the idea that black holes are genuine thermodynamic objects with a well-defined thermodynamic entropy has become more and more popular. Surprisingly, arguments that justify this assumption are both sparse and rarely convincing. Most of them rely on an…
There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity TdS = dE + PdV. We study this approach further and generalize the results to two more generic cases within the context of general relativity: (i) stationary axis-symmetric horizons and (ii) time dependent evolving horizons. In both the cases, the near horizon structure of Einstein …
We study spacetime thermodynamics for non-equilibrium processes. We first generalize the formulation of spacetime thermodynamics by using an observer outside the horizon. Then we construct the entropy balance equation of spacetime thermodynamics for non-equilibrium processes in f(R) gravity. The coefficients of the expansion and shear terms are equal to the viscosities of the black hole membrane paradigm, and a new entropy production term appears.
