Novel thermodynamic inequality for rotating AdS black holes

We propose a new thermodynamic inequality for stationary and asymptotically Anti-de Sitter rotating black holes, $4\pi J^2/(3MV)<1$. This inequality is derived by analyzing the roots of the identity relating the thermodynamic variables, ensuring the avoidance of naked singularities, and consequently preventing violations of the cosmic censorship conjecture. We examine the Kerr-AdS black hole as well as uncharged rotating AdS black strings, and find strong supporting evidence for the inequality across different horizon topologies. Using this inequality, we further demonstrate that the reverse isoperimetric inequality (${\cal R}\geq 1$), remains unchanged, in the presence of rotation. Our investigations of a broad class of black hole solutions provide additional confirmation of the proposed inequality. Assuming that the reverse isoperimetric inequality in the presence of rotation continues to hold in higher dimensions, we conjecture the corresponding higher-dimensional generalization of the inequality.