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.
We propose a new definition of "horizon molecules" in Causal Set Theory following pioneering work by Dou and Sorkin. The new concept applies for any causal horizon and its intersection with any spacelike hypersurface. In the continuum limit, as the discreteness scale tends to zero, the leading behaviour of the expected number of horizon molecules is shown to be the area of the horizon in discreteness units, up to a dimension dependent factor of order one. We also determine the first order corrections to the continuum value, and show how such corrections can be exploited to obtain further geome…
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…
The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a "first law" for variations to nearby solutions. The latter relates the variations of t…
Comments on "Thermodynamics and/of horizons : A comparison of Schwarzschild, Rindler and de Sitter spacetimes" (ArXiv : gr-qc/0202078), by T.Padmanabhan
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 analyse the causal aspects of evolving marginally trapped surfaces in a D-dimensional spherically symmetric spacetime, sourced by perfect fluid with a cosmological constant. The norm of the normal to the marginally trapped tube is shown to be the product of lie derivatives of the expansion parameter of future outgoing null rays along the incoming and outgoing null directions. We obtain a closed form expression for this norm in terms of principal density, pressure, areal radius and cosmological constant. For the case of a homogeneous fluid distribution, we obtain a simple form…
The horizon structure and thermodynamics of hairy spherically symmetric black holes generated by the gravitational decoupling method are carefully investigated. The temperature and heat capacity of the black hole is determined, as well as how the hairy parameters affect the thermodynamics. It allows the analysis of the thermal stability and the possible existence of a remanent black hole. We also calculate the Hawking radiation corrected by the generalized uncertainty principle. For such we consider the emission of fermions and apply the tunneling method to the generalized Dirac equation. It s…
Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
本文重新讨论了弗里德曼方程与热力学热力学第一定律之间的关系。我们发现，Hayward首先提出的处理动态黑洞“外“俘获视界的统一第一定律，可以用于FRW宇宙的视视界（FRW宇宙学中的一种“内”俘获视界）。我们讨论了三种引力理论：爱因斯坦理论、洛夫洛克理论和标量张量理论。在爱因斯坦理论中，热力学热力学第一定律在视视界上总是满足的。在Lovelock理论中，将高阶导数项作为有效的能量动量张量，我们发现这种方法可以给出与黑洞视界相同的熵公式。这意味着克劳修斯关系对洛夫洛克理论成立。在标量-张量引力中，我们发现，通过使用相同的过程，克劳修斯关系不再成立。这表明标量张量引力下FRW宇宙的视视界对应于一个非平衡态热力学系统。我们使用Eling { \it et al.}来对付$f(R)$引力。
Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
视界的引力动力学和热力学之间有一个有趣的类比。在广义相对论的情况下，以及更广泛的一类Lanczos-Lovelock引力理论的情况下，可以将任何球对称视界附近的场方程解释为热力学恒等式TdS = dE + PdV。我们进一步研究了这种方法，并将结果推广到广义相对论的背景下，两个更一般的情况下：（i）静态轴对称的地平线和（ii）时间依赖的演变地平线。在这两种情况下，爱因斯坦方程的近视界结构都可以表示为视界虚位移下的热力学恒等式。这一结果表明，引力动力学的热力学解释并不局限于球对称或静态的视野，而是相当普遍的性质，并表明引力和热力学之间更深层次的联系。
Gravitational Entropy And The Second Law of Thermodynamics for Causal Observers
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究院物理学院）；Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院物理系）
The recently proposed effective equation of motion for the $4D$- Einstein-Gauss-Bonnet gravity admits a static black hole solution that has, like the Rissner-Nordström charged black hole, two horizons instead of one for the Schwarzschild black hole. This means that the central singularity is timelike instead of spacelike. It should though be noted that in $D\geq5$, the solution always admits only one horizon like the Schwarzshild solution. In the equation defining the horizon, the rescaled Gauss-Bonnet coupling constant appears as a new 'gravitational charge' with a repulsive effect to cause i…
