Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory

Koga, Jun Ichirou; Maeda, Kei Ichi

doi:10.1103/physrevd.58.064020

Cited by 59 publications

(81 citation statements)

References 30 publications

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“…There are lot of arguments on the fact that which of these two frames can be considered as more physical one [11,12] (also see the reviews [13,14] to get more insights). * krishnakanta@iitg.ernet.in † ashmita.phy@gmail.com ‡ bibhas.majhi@iitg.ernet.in There is another controversial aspect of this theory which states whether the conformal equivalence of the action in the two frames is merely a mathematical equivalence or this equivalence is also reflected in the dynamical [15][16][17][18] and the underlying thermodynamic aspects as well [19][20][21][22][23] (also see the recent papers [24][25][26][27][28], which discusses on the equivalence of the two frames in the quantum level). There are a few unsolved issues such as, what are the explicit covariant expressions of the physical quantities (energy, entropy, temperature) and how they are connected in the two frames.…”

Section: Introductionmentioning

confidence: 99%

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

2018

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We revisit the thermodynamic aspects of the scalar-tensor theory of gravity in the Jordan and in the Einstein frame. Examining the missing links of this theory carefully, we establish the thermodynamic descriptions from the conserved currents and potentials by following both the Noether and the Abbott-Deser-Tekin (ADT) formalism. With the help of conserved Noether current and potential, we define the thermodynamic quantities, which we show to be conformally invariant. Moreover, the defined quantities are shown to fit nicely in the laws of (the first and the second) black hole thermodynamics formulated by the Wald's method. We stretch the study of the conformal equivalence of the physical quantities in these two frames by following the ADT formalism. Our further study reveals that there is a connection between the ADT and the Noether conserved quantities, which signifies that the ADT approach provide the equivalent thermodynamic description in the two frames as obtained in Noether prescription. Our whole analysis is very general as the conserved Noether and ADT currents and potentials are formulated off-shell and the analysis is exempted from any prior assumption or boundary condition.PACS numbers:

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Section: Introductionmentioning

confidence: 99%

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

2018

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“…(4.1). In addition, it has been proven [14] that the Noether charge Q H [ξ (h) ] conjugate to the Killing vector ξ a (h) , which gives the entropy of a black hole, also remains unchanged under the Legendre transformation. Then, we can employ the same method as shown in Sec.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…In the case of an asymptotically flat black hole, it has been proven [13,14] that the entropy of a black hole in the original frame and that in the Einstein frame coincide with each other. …”

Section: The First Lawmentioning

confidence: 99%

First law of AdS black holes in higher curvature gravity

Koga

2005

Phys. Rev. D

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We consider the first law of black hole thermodynamics in an asymptotically anti-de Sitter spacetime in the class of gravitational theories whose gravitational Lagrangian is an arbitrary function of the Ricci scalar. We first show that the conserved quantities in this class of gravitational theories constructed through conformal completion remain unchanged under the conformal transformation into the Einstein frame. We then prove that the mass and the angular momenta defined by these conserved quantities, along with the entropy defined by the Noether charge, satisfy the first law of black hole thermodynamics, not only in Einstein gravity but also in the higher curvature gravity within the class under consideration. We also point out that it is naturally understood in the symplectic formalism that the mass satisfying the first law should be necessarily defined associated with the timelike Killing vector nonrotating at infinity. Finally, a possible generalization into a wider class of gravitational theories is discussed.

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“…(35) and (36), but in the second variation of the horizon-entropy for causal horizons, through eqs. (28) and (31). If the right hand side of (38) ever becomes positive then the horizon-entropy of the quasi-local horizons will immediately start to decrease, but the change of horizon-entropy of a causal horizon may still increase because in this case it only influences the second variation of the horizon-entropy.…”

Section: Brans-dicke Theorymentioning

confidence: 99%

The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions

Faraoni

Nielsen

2011

Class. Quantum Grav.

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Abstract. 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 show, using this new definition, how to locate cosmological horizons in flat Minkowski space with varying units, which is physically identified with a spatially flat FLRW spacetime.

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Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory

Cited by 59 publications

References 30 publications

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

First law of AdS black holes in higher curvature gravity

The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions

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