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Entropy 2011, 13(12), 1967-1991; doi:10.3390/e13121967
Article

Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

1,2,*  and 1
1 Department of Mathematics and Computer Science, University of Warmia and Mazury, Słoneczna 54,10-710 Olsztyn, Poland 2 A.F.Ioffe Physico-Technical Institute, Polytekhnicheskaya 26, 194021 St. Petersburg, Russia
* Author to whom correspondence should be addressed.
Received: 3 August 2011 / Revised: 14 November 2011 / Accepted: 16 November 2011 / Published: 28 November 2011
(This article belongs to the Special Issue Black Hole Thermodynamics)
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Abstract

We address the question of thermodynamics of regular cosmological spherically symmetric black holes with the de Sitter center. Space-time is asymptotically de Sitter as r → 0 and as r → ∞. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant: 8πGTμν = Λδμν as r → 0, 8πGTμν = λδμν as r → ∞ with λ < Λ. It represents an anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. In the range of the mass parameter Mcr1 ≤ M ≤ Mcr2 it describes a regular cosmological black hole. Space-time in this case has three horizons: a cosmological horizon rc, a black hole horizon rb < rc, and an internal horizon ra < rb, which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. We present the basicfeatures of space-time geometry and the detailed analysis of thermodynamics of horizons using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. We find that in a certain range of parameters M and q =√Λ/λ there exist a global temperature for an observer in the R-region between the black hole horizon rb and cosmological horizon rc. We show that a second-order phase transition occurs in the course of evaporation, where a specific heat is broken and a temperature achieves its maximal value. Thermodynamical preference for a final point of evaporation is thermodynamically stable double-horizon (ra = rb) remnant with the positive specific heat and zero temperature.
Keywords: space-time horizons; regular black hole; evaporation; black hole remnants space-time horizons; regular black hole; evaporation; black hole remnants
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Dymnikova, I.; Korpusik, M. Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior. Entropy 2011, 13, 1967-1991.

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