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Galaxies 2015, 3(1), 53-71; doi:10.3390/galaxies3010053

Thermodynamic Relations for the Entropy and Temperature of Multi-Horizon Black Holes

1,2,* , 2
and
2,3
1
School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
2
School of Physics, Nankai University, Tianjin 300071, China
3
State Key Laboratory of ITP, ITP-CAS, Beijing 100190, China 
*
Author to whom correspondence should be addressed.
Academic Editor: Lorenzo Iorio
Received: 12 October 2014 / Revised: 26 January 2015 / Accepted: 28 January 2015 / Published: 2 February 2015
(This article belongs to the Special Issue Advances in Gravitational Research)
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Abstract

We present some entropy and temperature relations of multi-horizons, even including the “virtual” horizon. These relations are related to the product, division and sum of the entropy and temperature of multi-horizons. We obtain the additional thermodynamic relations of both static and rotating black holes in three- and four-dimensional (A)dS spacetime. Especially, a new dimensionless, charge-independence and T+S+ = T_S_-like relation is presented. This relation does not depend on the mass, electric charge, angular momentum and cosmological constant, as it is always a constant. These relations lead us to obtaining some interesting thermodynamic bounds of entropy and temperature, including the Penrose inequality, which is the first geometrical inequality of black holes. Besides, based on these new relations, one can obtain the first law of thermodynamics and the Smarr relation for all horizons of a black hole. View Full-Text
Keywords: black holes; thermodynamic relations; thermodynamic bound; thermodynamic laws; classical theories of gravity black holes; thermodynamic relations; thermodynamic bound; thermodynamic laws; classical theories of gravity
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. (CC BY 4.0).

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Xu, W.; Wang, J.; Meng, X.-H. Thermodynamic Relations for the Entropy and Temperature of Multi-Horizon Black Holes. Galaxies 2015, 3, 53-71.

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