Thermodynamics and Van der Waals phase transition of charged black holes in flat spacetime via Rényi statistics
Chatchai Promsiri, Ekapong Hirunsirisawat, Watchara Liewrian
Abstract
The phase structure and critical phenomena of the $3+1$ dimensional charged black holes in asymptotically flat spacetime are investigated within the R\'enyi statistics. As the nonextensive parameter $\ensuremath{\lambda}$ above zero, a charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation and have a Hawking--Page phase transition. This gives more evidence supporting the proposed conjectured equivalence between the black hole thermodynamics in asymptotically flat spacetime via R\'enyi statistics and that in asymptotically anti--de Sitter (AdS) spacetime via Gibbs--Boltzmann statistics. 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 the Smarr formula, the thermodynamic pressure $P$ and volume $v$ of a charged black hole are found to be related to $\ensuremath{\lambda}$. The thermodynamics of asymptotically flat charged black holes via R\'enyi statistics has the Van der Waals phase structure, $P\ensuremath{-}v$ criticality and universal constant, in a similar way as that of asymptotically AdS charged black hole via Gibbs--Boltzmann statistics. This raises an interesting question of how $\ensuremath{\lambda}$ in the former system relates to $|\mathrm{\ensuremath{\Lambda}}|$ in the latter one.