Abstract
The phase structure and critical phenomena of the 3+1 dimensional charged black holes in asymptotically flat spacetime are investigated in terms of thermodynamic properties within the R\'enyi statistics. With this approach as the non-extensive parameter above zero, we find that the charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation, and have a Hawking-Page phase transition in the same way in the case of AdS charged black hole. This gives more evidence supporting the proposal that there exists an equivalence between the black hole thermodynamics in asymptotically flat spacetime via R\'enyi statistics and that in asymptotically AdS spacetime via Gibbs-Boltzmann statistics, proposed by Czinner et al. However, the present work also provides another aspect of supporting evidence through exploring the extended phase space within the R\'enyi statistics. Working on a modified version of Smarr formula, the thermodynamic pressure $P$ and volume $v$ of a charged black hole are found to be related to the non-extensive parameter. The resulting $P-v$ diagram indicates that the thermodynamics of charged black holes in asymptotically flat spacetime via R\'enyi statistics has the Van der Waals phase structure, equivalent to that in asymptotically AdS spacetime via Gibbs-Boltzmann statistics.
Highlights
AND MOTIVATIONSIn general relativity, a black hole was initially expected to be a dark object as a result of the existence of the event horizon inside, which nothing can escape
We investigate the thermodynamics of charged black holes in asymptotically flat spacetime or RNflat via an alternative Renyi entropy both in the grand canonical and canonical ensembles
Applying the Renyi statistics, our results indicate that it is possible, with 0 < λ < 1, to have the small and large black hole branches in the grand canonical ensemble while this cannot occur in the GB statistics approach
Summary
A black hole was initially expected to be a dark object as a result of the existence of the event horizon inside, which nothing can escape. The thermodynamic stability of Schwarzschild and Kerr black holes in asymptotically flat spacetime were investigated via Renyi statistics in [23,24] Their works have shown that the black holes in asymptotically flat spacetime can be in a stable equilibrium with the heat bath at a fixed temperature ensemble at a positive nonextensive parameter λ 1⁄4 1 − q. In the present paper, being motivated by the nonextensive nature of black hole entropy and the VdW-like phase structure of a charged black hole in the AdS background in the extended phase space approach, we explore the thermodynamics of the 3 þ 1 dimensional Reissner–.
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