Black hole mechanics and thermodynamics in the light of Weyl transformations

Hammad, Fayçal; Massé, Étienne; Labelle, Patrick

doi:10.1103/physrevd.98.104049

Cited by 10 publications

(25 citation statements)

References 47 publications

(85 reference statements)

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“…5 Note that the requirement £ξẽ a µ = 0 that guarantees the equation ∂Ξ δQ[ξ] − iξΘ = 0 to hold in the conformal frame is now augmented by the requirement to also have £ξΩ =ξ µ∇ µΩ = 0. The latter is actually already guaranteed by the fact that ξ µ∇ µΩ = 0 is also the requirement for a Killing vector field to exist in the conformal frame [17].…”

Section: Summary and Discussionmentioning

confidence: 97%

Noether charge and black hole entropy in teleparallel gravity

Hammad¹,

Dijamco²,

Torres-Rivas³

et al. 2019

Phys. Rev. D

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The Noether charge associated to diffeomorphism invariance in teleparallel gravity is derived. It is shown that the latter yields the ADM mass of an asymptotically flat spacetime. The black hole entropy is then investigated based on Wald's prescription that relies on the Noether charge. It is shown that, like in general relativity, the surface gravity can be factored out from such a charge. Consequently, the similarity with the first law of thermodynamics implied by such an approach in general relativity does show up also in teleparallel gravity. It is found that, based on the expression of the first law of black hole mechanics, which is preserved in teleparallel gravity, entropy can thus be extracted from such a Noether charge. The resulting entropy can very naturally be expressed as a volume integral, though. As such, it is shown that the conformal issue that plagues the entropy-area law within general relativity does not arise in teleparallel gravity based on Wald's approach. The physics behind these features is discussed.

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Section: Summary and Discussionmentioning

confidence: 97%

Noether charge and black hole entropy in teleparallel gravity

Hammad¹,

Dijamco²,

Torres-Rivas³

et al. 2019

Phys. Rev. D

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“…[9] for a discussion on this issue), but is rather similar in spirit to Refs. [10][11][12][13][14]. The best way to reveal the true nature of any concept in spacetime physics -or, in this case, any incompatibility between two approaches towards understanding spacetime physics -is in fact to view the concept, or apply the approaches, in a deformed setting that is capable of "filtering out" purely geometric from purely material entities.…”

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confidence: 99%

“…These transformations leave spacetime coordinates intact but change a spacetime metric g ab into a new metricg ab = Ω 2 g ab , where the conformal factor Ω(x) is a spacetime-dependent, nonvanishing, and everywhere regular function. Indeed, such an approach has successfully been applied to probe the true nature of some of the well-known quasilocal definitions of energy in general relativity [10,11], to study the behavior of black holes and wormholes under conformal transformations [12], to investigate the requirement for violating the null energy condition by traversable wormholes under different settings [13] and, most importantly, to provide a different point of view on black hole mechanics and thermodynamics [14].…”

mentioning

confidence: 99%

“…In fact, in Ref. [14] it was shown that a Weyl conformal transformation renders the familiar analogy between black hole mechanics and thermodynamics ambiguous. It was emphasized there that this issue arises whenever one mixes purely geometric concepts with purely material ones.…”

mentioning

confidence: 99%

“…On the basis of this conflict, it was argued in Ref. [14] that when talking about black hole thermodynamics it would be more accurate to distinguish between the black hole's "material" thermodynamics and the black hole's "geometric" thermodynamics, for conformal transformations do not allow mixing between the two.…”

mentioning

confidence: 99%

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More on spacetime thermodynamics in the light of Weyl transformations

Hammad

Dijamco

2019

Phys. Rev. D

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It was recently found that, after performing a Weyl conformal transformation, the familiar analogy between black hole mechanics and black hole thermodynamics becomes ambiguous. It was argued that this fact can be traced back to the fundamental dichotomy between matter and geometry, which is at the heart of Einstein's field equations. As a further study of this issue, we investigate here the general link between spacetime thermodynamics and Weyl transformations from two other angles. We first examine the conformal behaviour of the horizon entropy within Wald's approach based on the fundamental diffeomorphism symmetry of pure geometry. We then revisit -using Weyl transformations -Jacobson's derivation of Einstein's field equations, the starting point of which is precisely built on the fundamental dichotomy between matter and geometry. As a result, we show that in order for Jacobson's approach to be able to yield the right Einstein field equations in the conformal frame, a specific conformal behavior of the horizon temperature and its entropy -different from what Wald's approach implies -is required. The two approaches to spacetime thermodynamics become thus incompatible in the conformal frame. In addition, we show -in greater detail in the conformal frame -that in the presence of a null dust the thermodynamics approach for extracting Einstein's field equations necessarily fails. An extensive discussion of the whole issue is given.

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Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations

2018

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We show that the violation of the null energy condition by matter, required by traversable wormholes, can be removed in spacetimes with torsion. In addition, we show that this violation can also be removed in the conformal frame obtained by a Weyl transformation. This comes about because both conformally transformed wormholes and wormholes in spacetimes with torsion become sustained thanks to a combination of "normal" matter, that satisfies the null energy condition, and an induced "geometric" energy-momentum tensor that is able to greatly violate the null energy condition.PACS numbers: 04.50.Kd, 04.90.+e, 02.40.Ky * fhammad@ubishops.ca † Etienne.Masse@usherbrooke.ca ‡ plabelle@crc-lennox.qc.ca 1 Throughout the paper, we set 8πG = = c = 1.

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Black hole mechanics and thermodynamics in the light of Weyl transformations

Cited by 10 publications

References 47 publications

Noether charge and black hole entropy in teleparallel gravity

Noether charge and black hole entropy in teleparallel gravity

More on spacetime thermodynamics in the light of Weyl transformations

Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations

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