Horizon entropy and higher curvature equations of state

Guedens, Raf; Jacobson, Ted; Sarkar, Sudipta

doi:10.1103/physrevd.85.064017

Cited by 51 publications

(90 citation statements)

References 32 publications

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“…with κ a function corresponding to the normal surface gravity, which a priori represents a different notion of surface gravity than the inaffinity surface gravity defined through the geodesic equation (21). For our horizon to be a Killing horizon, we further demand the null vector field χ µ to be a Killing vector field; we can then use (20)…”

Section: Horizon Propertiesmentioning

confidence: 99%

“…It was possible to obtain the equation of motion for f (R) theory [19,20] after modification of the Clausius equation to add internal entropy production terms but there were many technical hindrances for a further generalization using just the proportionality of entropy with horizon area. In [21,22] a further generalization of this result for higher derivative theories of gravity was achieved by assuming the entropy to have a form similar to the Noether charge associated to the diffeomorphisms of the theory.…”

Section: Introductionmentioning

confidence: 99%

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Spacetime thermodynamics in the presence of torsion

2017

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It was shown by Jacobson in 1995 that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. With the aim to understand if such thermodynamical description is an intrinsic property of gravitation, many attempts have been done so far to generalise this treatment to a broader class of gravitational theories. Here we consider the case of the Einstein-Cartan theory as a prototype of theories with non-propagating torsion. In doing so, we study the properties of Killing horizons in the presence of torsion, establish the notion of local causal horizon in Riemann-Cartan spacetimes, and derive the generalised Raychaudhuri equation for this kind of geometries. Then, starting with the entropy that can be associated to these local causal horizons, we derive the Einstein-Cartan equation by implementing the Clausius equation. We outline two ways of proceeding with the derivation depending on whether we take torsion as a geometric field or as a matter field. In both cases we need to add internal entropy production terms to the Clausius equation as the shear and twist cannot be taken to be zero a priori for our setup. This fact implies the necessity of a non-equilibrium thermodynamics treatment for the local causal horizon. Furthermore, it implies that a non-zero twist at the horizon will in general contribute to the Hartle-Hawking tidal heating for black holes with possible implications for future observations.Comment: 18 page

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Section: Horizon Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spacetime thermodynamics in the presence of torsion

2017

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“…Recently, this scenario has been extensively investigated in various approaches [38][39][40][41][42][43][44][45][46][47][48]. In particular, based on the assumption that the gravitational theory can be described by entropy force [49], which has been widely interested by many theorists [40,[50][51][52][53][54][55][56][57][58][59][60][61][62][63], the authors in [40] proposed that an interesting setup was that the modified dispersion relation prevented the energy density of the matter contents from diverging at high energy level such that the modified Friedmann equation with the bouncing effect can be derived successfully from the Clausius relation, where the singularity of the corresponding spacetime was free.…”

Section: Introductionmentioning

confidence: 99%

Bouncing universe with modified dispersion relation

Pan¹,

Huang²

2016

Gen Relativ Gravit

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In this paper, employing the modified dispersion relation, we have derived the general modified Friedmann equations and the corresponding modified entropy relations for the FriedmannRobertson-Walker (FRW) Universe. In this setup, we find that when the big bounce happens, its energy scale and its corresponding modified entropy behavior are sensitive to the value of k.In contrast to the previous work with k = 0, our work mainly demonstrates that the bouncing behavior for the closed Universe with k = 1 appears at the normal energy limit of the modified dispersion relation introduced, and when bouncing phenomenon is in presence, its modified entropy is just equal to zero. Surprisingly, when k = −1, the bouncing behavior is in absence. * Electronic address: wjpan˙zhgkxy@163.com † Electronic address: ychuang@bjut.edu.cn

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“…The authors of ref. [15] used a careful construction of the geometry of local causal horizon (LCH) and the approximate Killing vector field constructed in ref. [16].…”

Section: Introductionmentioning

confidence: 99%

Higher derivative gravity: Field equation as the equation of state

2016

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One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.

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Horizon entropy and higher curvature equations of state

Cited by 51 publications

References 32 publications

Spacetime thermodynamics in the presence of torsion

Spacetime thermodynamics in the presence of torsion

Bouncing universe with modified dispersion relation

Higher derivative gravity: Field equation as the equation of state

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