Horizon thermodynamics from Einstein's equation of state

Hansen, Devin; Kubizňák, David; Mann, Robert B.

doi:10.1016/j.physletb.2017.04.076

Cited by 17 publications

(52 citation statements)

References 40 publications

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“…Coupling the theory to Maxwell or scalar fields [41] could lead to further examples of new, novel phase transitions such as the recently discovered superfluid-like transition [42]. It should also be possible to cast the theory in terms of horizon thermodynamics [43], at least for a certain class of matter actions, e.g. a Maxwell field.…”

Section: Discussionmentioning

confidence: 99%

Generalized quasitopological gravity

2017

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We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possess the following remarkable properties: i) it has a well-defined Einstein gravity limit ii) it admits 'Schwarzschild-like' solutions characterized by a single metric function iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein's gravity iv) Lovelock and quasi-topological gravities, as well as the recently developed Einsteinian cubic gravity ArXiv:1607.06463 in four dimensions, are recovered as special cases. We perform a brief analysis of asymptotically flat black holes in this theory and study their thermodynamics.

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Section: Discussionmentioning

confidence: 99%

Generalized quasitopological gravity

2017

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“…These results has been generalized to the case of nonzero chemical potential [15].When assuming a horizon equation of state, one can get a horizon first law by considering a virtual displacement, from which the entropy can be obtained [11]. Recently a new horizon first law was suggested in [16], in this approach both the entropy and the free energy are derived concepts, and from which the standard horizon first law is recovered by a Legendre projection. For Einstein gravity and Lovelock gravity which only give rise to second-order field equation for all metric components, their results have establish a way of how to formulate consistent black hole thermodynamic without conserved charges.…”

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confidence: 99%

Horizon thermodynamics in f(R) theory

Zheng

Yang

2018

Eur. Phys. J. C

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We investigate whether the new horizon first law proposed recently still work in f (R) theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in f (R) theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in f (R) theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.It is well-known that there is a profound connection between gravity and thermodynamics: the spacetime with horizons can be described by thermodynamic laws. Bekenstein found that the area of a black hole can be seen as its entropy [1]. Four laws of black hole mechanics were proposed in [2]. It has been shown that the entropy of a black hole can be taken as the Noether charge associated with the diffeomorphism invariance of the theory of gravity [3,4]. From the first law of thermodynamics Einstein equation has been derived in [5]. Non-equilibrium thermodynamics of spacetime has been investigated in [6]. By using a more general definition of the Noether charge entropy, the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation δQ = T δS [7]. This attempt also has been considered in modified gravity theories: such as f (R) theory [8], Lancos-Lovelock gravity [9], and the scalar-Gauss-Bonnet gravity [10]. In [11], a general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes was developed. For stationary axis-symmetric horizons and time dependent evolving horizons, it has been shown that the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon [12]. It also has been shown 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 [13]. All these studies were based on some assumptions, such as horizon, null surfaces, Unruh temperature, and so on. In [14], without assuming a temperature or a horizon the thermal entropy density has been obtained for any arbitrary spacetime, implying that gravity possesses thermal effects, or, thermal entropy density possesses effects of gravity. These results has been generalized to the case of nonzero chemical potential [15].When assuming a horizon equation of state, one can get a horizon first law by considering a virtual displacement, from which the entropy can be obtained [11]. Recently a new horizon first law was suggested in [16], in this approach both the entropy and the free energy are derived concepts, and from which the standard horizon first law is recovered by a Legendr...

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“…As a matter of fact, the equation (1) can be rewritten as δE = (T S ′ + P V ′ ) δr + , where the primes stands for the derivative with respected to r + . This makes the terms 'heat' and 'work' confused and results to a 'vacuum interpretation' of the first law (1) [22]. To avoid the problems mentioned above, a new horizon first law was proposed in [22], by varying the horizon equation of state with the temperature T and the pressure P as independent thermodynamic quantities…”

Section: The New Horizon First Lawmentioning

confidence: 99%

“…This new horizon first law has practical utility and provides further evidence for the connection between gravity and thermodynamics. In 4-dimensional Einstein gravity, we briefly review this approach to explain how it works [22]. Considering the geometry of a static spherically symmetric black hole, which is given by…”

Section: The New Horizon First Lawmentioning

confidence: 99%

“…Using the first law of the horizon, one can derived the entropy and energy of black hole in Einstein gravity [11]. Recently, as shown in [21], the entropy and energy of black hole in f (R) theories can be obtained simultaneously though the new horizon first law which was proposed in [22]. Here we will consider the more complicated case: for the general spherically symmetric black hole we hope to obtain the energy and entropy in f (R) theories, which can reduce to the results in [16,21] for some special cases.…”

Section: Introductionmentioning

confidence: 99%

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Entropy and Energy of Static Spherically Symmetric Black Hole in f(R) Theory

Zheng

Yang

2020

Universe

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We consider the new horizon first law in f (R) theory with general spherically symmetric black hole. We derive the general formulas to computed the entropy and energy of the black hole, which are consistent with the results obtained in the literatures. For applications, some nontrivial black hole solutions in some popular f (R) theories are investigated, the entropies and the energies of black holes in these models are first calculated.

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Horizon thermodynamics from Einstein's equation of state

Cited by 17 publications

References 40 publications

Generalized quasitopological gravity

Generalized quasitopological gravity

Horizon thermodynamics in f(R) theory

Entropy and Energy of Static Spherically Symmetric Black Hole in f(R) Theory

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