A note on entropy of de Sitter black holes

Bhattacharya, Sourav

doi:10.1140/epjc/s10052-016-3955-6

Cited by 46 publications

(49 citation statements)

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“…Indeed, on the horizon ∆ r = 0, we can write using M loc (r) a transcendental equation, Linear variation of the above equation and use of Eq. (50) gives that the first term on the right hand side of Eq. (51) is always greater than or equal to zero.…”

Section: Generalized Area Theorem For Kerr-de Sittermentioning

confidence: 99%

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Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

Bhattacharya

2018

Phys. Rev. D

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We investigate various aspects of energy extraction via the Penrose process in the Kerr-de Sitter spacetime. We show that the increase in the value of a positive cosmological constant, Λ, always reduces the efficiency of this process. The Kerr-de Sitter spacetime has two ergospheres -associated with the black hole and the cosmological event horizons. We prove by analysing turning points of the trajectory that the Penrose process in the cosmological ergoregion is never possible. We next show that in this process both black hole and cosmological event horizons' areas increase, the later becomes possible when the particle coming from the black hole ergoregion escapes through the cosmological event horizon. We identify a new, local mass function instead of the mass parameter, to prove this generalized area theorem. This mass function takes care of the local spacetime energy due to the cosmological constant as well, including that arises due to the frame dragging effect due to spacetime rotation. While the current observed value of Λ is much tiny, its effect in this process could be considerable in the early universe scenario endowed with a rather high value of it, where the two horizons could have comparable sizes. In particular, the various results we obtain here are also evaluated in a triply degenerate limit of the Kerr-de Sitter spacetime we find, in which radial values of the inner, the black hole and the cosmological event horizons are nearly coincident.The existence of such negative energy particles gives rise to a classical mechanism for energy extraction from a black hole, namely the Penrose process, as follows [1,2,3], also references therein. Let a particle carrying positive energy enters the ergoregion of a Kerr black hole. We imagine that it breaks into two pieces there -one carrying negative energy and the other, positive. The negative energy particle enters the BEH and the positive energy particle, after reaching a turning point, comes out of the ergosphere and finally gets intercepted by an outside observer. With respect to such an observer the usual (positive) energy conservation must be valid. Thus it is clear that the ejecta will carry more energy than the initial incoming particle, effectively extracting energy from the black hole. It turns out that the energy thus extracted is largely rotational and the process can only continue until the black hole settles down into the Schwarzschild spacetime, where no ergosphere is present.Since the Penrose process reduces more the rotation of a black hole than its mass, a Kerr black hole can never become a naked curvature singularity under this process, see [4] for a formal proof of this. In [5], it was proved that the black hole horizon area must increase under this process, thereby providing evidence in favour of the second law of black hole mechanics. We further refer our reader to [6,7] for various inequalities (respectively, the Wald and the Bardeen-Press-Teukolsky inequality) regarding the local speed of the fragments within the ergoregion. In order tha...

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Section: Generalized Area Theorem For Kerr-de Sittermentioning

confidence: 99%

“…[40,41,43] and references therein). We refer our reader to [50] for a derivation of such total entropy using near horizons' conformal symmetries. We also refer our reader to [54] for a proposal of further modifying such entropy via correlation between the two horizons.…”

Section: Introductionmentioning

confidence: 99%

Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

Bhattacharya

2018

Phys. Rev. D

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“…In the second approach taken [20,22,23,24] (for a nice review on both approaches, see [25]), it was assumed instead that the black-hole mass plays the role of the enthalpy of the system (M = −H), the cosmological constant that of the pressure (P = Λ/8π) while the entropy is still S = S h + S c . In that case, the effective temperature of the system was found to have the expression…”

Section: The Gravitational Backgroundmentioning

confidence: 99%

“…This problem may be ignored in the limit of a small cosmological constant, when the two horizons are located far away, but it worsens when the cosmological constant takes a large value. In a new approach adopted in a series of works [20,21,22,23,24] (see also [25] for a review), the notion of the effective temperature for the SdS spacetime was proposed that implements both the black-hole and the cosmological horizon temperatures (for a number of additional works on SdS thermodynamics, see [26]- [45]).…”

Section: Introductionmentioning

confidence: 99%

Schwarzschild–de Sitter spacetime: The role of temperature in the emission of Hawking radiation

Παππάς

Kanti

2017

Physics Letters B

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We consider a Schwarzschild-de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates. 1

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“…There are currently two kinds of viewpoints. In references [35,36,[41][42][43][44][45], the authors think that dS space-time's entropy is the sum of the two horizons' S = S + + S c (S + and S c represent the entropy of black hole horizon and cosmological horizon, respectively), but, in reference [40,45], they think that it is the difference of two horizons' S = S c − S + . Different effective temperatures are obtained for the same de Sitter space-time due to different values of entropy.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity

Zhang

et al. 2020

Eur. Phys. J. C

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On the basis of the state parameter of de Sitter space-time satisfying the first law of thermodynamics, we can derive some effective thermodynamic quantities. When the temperature of the black hole horizon is equal to that of the cosmological horizon, we think that the effective temperature of the space-time should have the same value. Using this condition, we obtain a differential equation of the entropy of the de Sitter black hole in the higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity. Solving the differential equation, we obtain the corrected entropy and effective thermodynamic quantities of the de Sitter black hole. The results show that for multi-parameter black holes, the entropy satisfied differential equation is invariable with different independent state parameters. Therefore, the entropy of higher-dimensional dS black holes in dRGT massive gravity is only a function of the position of the black hole horizon, and is independent of other state parameters. It is consistent with the corresponding entropy of the black hole horizon and the cosmological horizon. The thermodynamic quantities of self-consistent de Sitter space-time are given theoretically, and the equivalent thermodynamic quantities have the second-order phase transformation similar to AdS black hole, but unlike AdS black hole, the equivalent temperature of de Sitter space-time has a maximum value. By satisfying the requirement of thermodynamic equilibrium and stability of space-time, the conditions for the existence of dS black holes in the universe are obtained.PACS numbers:

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A note on entropy of de Sitter black holes

Cited by 46 publications

References 47 publications

Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

Kerr-de Sitter spacetime, Penrose process, and the generalized area theorem

Schwarzschild–de Sitter spacetime: The role of temperature in the emission of Hawking radiation

Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity

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