Black hole evaporation in conformal (Weyl) gravity

Xu, Hao; Yung, Man‐Hong

doi:10.1016/j.physletb.2019.04.036

“…The black hole evaporation process in = 1 and d = 4, 5 is different from Schwarzschild-AdS because of the existence of the state T = 0 and the third law of the black hole thermodynamics. The black hole evaporation in HL gravity is different from the other higher derivative gravity theories, such as the conformal (Weyl) gravity [48,49] and the Lovelock gravity [50], because the black hole mass in HL gravity can be written as M ∼ d−3 , thus according to the Stefan-Boltzmann law, the lifetime is in the order of…”

Section: Discussionmentioning

confidence: 96%

“…Therefore, it is important to study the various properties of HL black holes. In this work, we shall consider the black hole evaporation process in HL gravity and compare the results with the AdS black hole in Einstein gravity [12] or higher derivative gravity theories [48][49][50].…”

Section: Introductionmentioning

confidence: 99%

Black hole evaporation in Hořava–Lifshitz gravity

Xu

¹

,

Ong

²

2020

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Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter $$0\leqslant \epsilon ^2\leqslant 1$$ 0 ⩽ ϵ 2 ⩽ 1 . We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with $$d=4,5$$ d = 4 , 5 behave differently from $$d\geqslant 6$$ d ⩾ 6 . For the case of $$\epsilon =0$$ ϵ = 0 , in $$d=4,5$$ d = 4 , 5 , the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As $$d\geqslant 6$$ d ⩾ 6 , however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of $$\ell ^{d-1}$$ ℓ d - 1 , similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to $$\epsilon ^2=1$$ ϵ 2 = 1 ), though for the latter this holds for all $$d\geqslant 4$$ d ⩾ 4 . The case of $$0<\epsilon ^2<1$$ 0 < ϵ 2 < 1 is also qualitatively similar with $$\epsilon =0$$ ϵ = 0 .

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“…The pure AdS space-time, corresponding to M = − 1 2G k , cannot be reached just by black hole evaporation process. The second one is the difference from conformal (Weyl) gravity [41,42], where a final state with vanishing temperature that cannot be achieved in finite time also exists. However, in conformal (Weyl) gravity the final state corresponds to an extremal black hole with finite size, while in our case it corresponds to r + → 0.…”

Section: Inserting the Impact Factormentioning

confidence: 99%

Black hole evaporation in Lovelock gravity with diverse dimensions

Xu

¹

,

Yung

²

2019

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We investigate the black hole evaporation process in Lovelock gravity with diverse dimensions. By selecting the appropriate coefficients, the space-time solutions can possess a unique AdS vacuum with a fixed cosmological constant Λ = − (d−1)(d−2) 2ℓ 2 . The black hole solutions can be divided into two cases: d > 2k + 1 and d = 2k + 1. In the case of d > 2k + 1, the black hole is in an analogy with the Schwarzschild AdS black hole, and the life time is bounded by a time of the order of ℓ d−2k+1 , which reduces Page's result on the Einstein gravity in k = 1. In the case of d = 2k + 1, the black hole resembles the three dimensional black hole. The black hole vacuum corresponds to T = 0, so the black hole will take infinite time to evaporate away for any initial states, which obeys the third law of thermodynamics. In the asymptotically flat limit ℓ → ∞, the system reduces to the pure Lovelock gravity that only possesses the highest k-th order term. For an initial mass M0, the life time of the black hole is in the order of M d−2k+1 d−2k−1 0 .

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“…Nevertheless, if we ignore these subtleties 6 , and consider the mass loss of GHS black hole to be governed only modified gravity theories, e.g., asymptotically safe gravity with higher derivative terms [48] and in conformal (Weyl) gravity [49] (note that entropy vanishes does not always imply zero area for modified gravity black holes). The usual third law applies to these black holes -they have infinite lifetime.…”

Section: A Charged and Dilaton Black Holes: Nonzero Mass Vs Nonzeromentioning

confidence: 99%

A complementary third law for black hole thermodynamics

Yao

¹

,

Hou

²

,

Ong

³

2019

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There are some examples in the literature, in which despite the fact that the underlying theory or model does not impose a lower bound on the size of black holes, the final temperature under Hawking evaporation is nevertheless finite and nonzero. We show that under some loose conditions, the black hole is necessarily an effective remnant, in the sense that its evaporation time is infinite. That is, the final state that there is nonzero finite temperature despite having no black hole remaining cannot be realized. We discuss the limitations, subtleties, and the implications of this result, which is reminiscent of the third law of black hole thermodynamics, but with the roles of temperature and size interchanged. We therefore refer to our result as the "complemetary third law" for black hole thermodynamics.

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Black hole evaporation in conformal (Weyl) gravity

Cited by 19 publications

References 79 publications

Black hole evaporation in Hořava–Lifshitz gravity

Black hole evaporation in Hořava–Lifshitz gravity

Black hole evaporation in Lovelock gravity with diverse dimensions

A complementary third law for black hole thermodynamics

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