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1.
We present a general procedure to construct the first law of thermodynamics on the apparent horizon and illustrate its validity by examining it in some extended gravity theories. Applying this procedure, we can describe the thermodynamics on the apparent horizon in Randall–Sundrum braneworld imbedded in a nontrivial bulk. We discuss the mass-like function which was used to link Friedmann equation to the first law of thermodynamics and obtain its special case which gives the generalized Misner–Sharp mass in Lovelock gravity. 相似文献
2.
We show that the recent tunneling formulas for black hole radiation in static, spherically symmetric spacetimes follow as a consequence of the first law of black hole thermodynamics and the area-entropy relation based on the radiation temperature. A tunneling formula results even if the radiation temperature is different from the one originally derived by Hawking and this is discussed in the context of the recent factor of 2 problem. In particular, it is shown that if the radiation temperature is higher than the Hawking temperature by a factor of two, thermodynamics then leads to a tunneling formula which is exactly the one recently found to be canonically invariant. 相似文献
3.
Haryanto M. Siahaan 《中国物理C(英文版)》2023,47(3):035105-035105-10
We study a charged Taub-NUT spacetime solution in the Dvali-Gabadadze-Porrati (DGP) brane. We show that the Reissner-Nordstrom-Taub-NUT-de Sitter solution of Einstein-Maxwell gravity solves the corresponding equations of motion, where the cosmological constant is related to the cross-over scale in the DGP model. Following the approach by Teitelboim in discussing the thermodynamics of de Sitter spacetime and the proposal by Wu et al. for a conserved charge associated with the NUT parameter, we obtain the generalized Smarr mass formula and the first law of thermodynamics of the spacetime. 相似文献
4.
Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ=T dS, where the heat flow δQ is the energy-supply of pure matter projecting on the vector ζ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/2πrA, the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit Hc→0, which recovers the Minkowski reference metric solution in the flat case, the generalized second law of thermodynamics holds if α3+4α4<0. Without this condition, even for the simplest model of dRGT massive cosmology with α3=α4=0, the generalized second law of thermodynamics could be violated. 相似文献
5.
《Comptes Rendus Physique》2018,19(5):337-340
Here we obtain explicit black hole solutions in Extension Gravity models with high-order derivative terms, while the Lichnerowicz-type theorem simplifies our analysis by vanishing Ricci's scalar curvature. We find out two explicit static, spherical solutions that satisfy the presented action: the first one is the same usual Schwarzschild solution and the other one is the new non-Schwarzschild solution. It means that Schwarzschild's solution following the no-hair theorem can describe any black hole object on each gravity theory. Without considering the first law of thermodynamics for it, we show that the non-Schwarzschild solution is depending on its set of constants, and then we consider its entropy and other thermodynamic parameters for specific values of the constants. 相似文献
6.
7.
Hawking radiation from the black hole in Ho?ava–Lifshitz gravity is discussed by a reformulation of the tunneling method given in Banerjee and Majhi (2009) [17]. Using a density matrix technique the radiation spectrum is derived which is identical to that of a perfect black body. The temperature obtained here is proportional to the surface gravity of the black hole as occurs in usual Einstein gravity. The entropy is also derived by using the first law of black hole thermodynamics. Finally, the spectrum of entropy/area is obtained. The latter result is also discussed from the viewpoint of quasi-normal modes. Both methods lead to an equispaced entropy spectrum, although the value of the spacing is not the same. On the other hand, since the entropy is not proportional to the horizon area of the black hole, the area spectrum is not equidistant, a finding which also holds for the Einstein–Gauss–Bonnet theory. 相似文献
8.
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 is evaluated from the validity of the unified first law and as a result there is a correction (in integral form) to the usual Bekenstein entropy. The other thermodynamical parameter namely temperature on the horizon is chosen as the recently introduced corrected Hawking temperature. The above thermodynamical analysis is done for homogeneous and isotropic flat FLRW model of the Universe. The restrictions for the validity of GSLT and the TE are presented in tabular form for each gravity theory. Finally, due to complicated expressions, the validity of GSLT and TE are also examined from graphical representation, using three Planck data sets. 相似文献
9.
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. 相似文献
10.
In this paper, the thermodynamics of the Friedmann–Lemaître–Robertson–Walker universe have been explored in f(R) theories of gravity with arbitrary matter-geometry coupling. The equivalence between the modified Friedmann equations with any spatial curvature and the first law of thermodynamics is confirmed, where the assumption of the entropy plays a crucial role. Then laws of thermodynamics in our considering case are obtained. They can reduce to the ones given in Einstein’s general theory of relativity under certain conditions. Moreover, a particular model is investigated through the obtained generalized second law of thermodynamics with observational results of cosmographic parameters. 相似文献
11.
Abhas Mitra 《Foundations of Physics》2011,41(9):1454-1461
We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve
proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation
as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum
gravity which apparently suggests thermodynamical properties even for a (singular) black hole. Having made such a clarification,
we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified
that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier. 相似文献
12.
A profound quantum-gravitational effect of space–time dimension running with respect to the size of space–time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of causal dynamical triangulation [hep-th/0505113] as well as in renormalization group approach to quantum gravity [hep-th/0508202]. Unfortunately, along these approaches the interpretation and the physical meaning of the effective change of dimension at shorter scales is not clear. The aim of this Letter is twofold. First, we find that box-counting dimension in face of finite resolution of space–time (generally implied by quantum gravity) shows a simple way how both the qualitative and the quantitative features of this effect can be understood. Second, considering two most interesting cases of random and holographic fluctuations of the background space, we find that it is random fluctuations that gives running dimension resulting in modification of Newton's inverse square law in a perfect agreement with the modification coming from one-loop gravitational radiative corrections. 相似文献
13.
With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first law of thermodynamics and Friedmann equation. 相似文献
14.
Ujjal Debnath 《International Journal of Theoretical Physics》2014,53(6):2108-2117
In this work, we have considered the Vaidya spacetime in null radiating fluid with perfect fluid in higher dimension and have found the solution for barotropic fluid. We have shown that the Einstein’s field equations can be obtained from Unified first law i.e., field equations and unified first law are equivalent. The first law of thermodynamics has also been constructed by Unified first law. From this, the variation of entropy function has been derived on the horizon. The variation of entropy function inside the horizon has been derived using Gibb’s law of thermodynamics. So the total variation of entropy function has been constructed at apparent and event horizons both. If we do not assume the first law, then the entropy on the both horizons can be considered by area law and the variation of total entropy has been found at both the horizons. Also the validity of generalized second law (GSL) of thermodynamics has been examined at both apparent and event horizons by using the first law and the area law separately. When we use first law of thermodynamics and Bekenstein-Hawking area law of thermodynamics, the GSL for apparent horizon in any dimensions are satisfied, but the GSL for event horizon can not be satisfied in any dimensions. 相似文献
15.
《Physica A》2006,369(2):432-438
We show, starting from first principles, that thermodynamics’ first law can be microscopically obtained for Fisher's information measure without need of invoking the adiabatic theorem. Further, it is proved that enforcing the Fisher-first law requirements in a process in which the probability distribution is infinitesimally varied is equivalent to minimizing Fisher's information measure subject to appropriate constraints. 相似文献
16.
J. Sadeghi J. Naji H. Vaez B. Khanpour 《International Journal of Theoretical Physics》2014,53(9):3089-3094
In this paper, we write modified Friedman-Robertson-Walkers (FRW) equation in the form of first law of thermodynamics at the apparent horizon. We consider the universe filled with the viscous fluid. Here we employ the general expression of temperature gravity and entropy at the apparent horizon of FRW universe and obtain the generalized first law of thermodynamics at the special condition for the modified FRW equation. The generalized first law of thermodynamics help us to arrange the α 1, α 2, β 1 and β 2 in modified Friedman-Robertson-Walkers equation. 相似文献
17.
We calculate the local energy and the energy density of the Reisner-Norstrm-anti-de-Sitter black hole, study the first law of thermodynamics and show the Smarr formula for the Born-Infeld-anti-de-Sitter black hole. Applying the first law of thermodynamics to the black hole region, we analyse the three energy exchange processes between the black hole region and the outer and the inner regions. 相似文献
18.
We consider Einstein gravity coupled to an U(1) gauge field for which the density is given by a power of the Maxwell Lagrangian. In d-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as d/4. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a
cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or
an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density,
the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities
of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we
obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law
of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking–Page
phase transition in spite of conformally invariant Maxwell field. 相似文献
19.
We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it is found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale rcof the 5-dimensional DGP model. 相似文献
20.
We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it is found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale rc of the 5-dimensional DGP model. 相似文献