Thermodynamics, stability and Hawking-Page transition of black holes from non-extensive statistical mechanics in quantum geometry

摘要

In this letter, the Tsallis theory of non-extensive statistical mechanics described by the parameter q > 0 is applied in loop quantum gravity to calculate the black hole entropy, following ref. [11]. The black hole entropy is derived in terms of the Bekenstein-Hawking law for a given horizon area of mass M and arbitrary real positive values of the Immirzi parameter (gamma). In this framework, it is shown that the black hole has a minimum temperature at M-min which relies on the q-parameter, and the specific heat of system is positive with M > M-min; this means that the large black hole is thermodynamically stable against radiation, in contrast to the standard result where all solutions appear to be unstable. This result is very similar to the ones announced from a black hole in Anti-de Sitter (AdS) space, where it is also proved that a Hawking-Page black hole phase transition results at a critical temperature which relies on the q parameter of the Tsallis formula. (C) 2019 The Authors. Published by Elsevier B.V.