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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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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