Novel thermodynamic inequality for rotating AdS black holes

Abstract

We propose a new thermodynamic inequality for stationary and asymptotically Anti-de Sitter charged and rotating black holes, $ 4πJ^2/(3MV)<1 $. This inequality is derived through an analysis of the roots of the identity which holds among the thermodynamic variables to avoid a naked singularity. We have analyzed the Kerr-AdS black hole and the asymptotically AdS uncharged and rotating black strings and find strong supporting evidence for different horizon topologies. Using this inequality we verify the validity of reverse isoperimetric inequality in its conventional form ($ {\cal R}\geq 1 $) in the presence of rotation. By examining a wide range of black hole solutions, we confirm the validity of the proposed inequality. Assuming that reverse isoperimetric inequality continues to hold in higher dimensions, and employing the intermediate refined reverse isoperimetric inequalities introduced in [Phys. Rev. Lett. 131, 241401] as guiding principles, we extend the inequality to higher-dimensional spacetimes.