Thermodynamics and Stability of Ultraspinning Black Holes
Ultraspinning black holes have attracted considerable attention due to their super-entropic nature, and previous analyses -- mostly restricted to neutral cases and high-temperature regimes -- have suggested that such black holes are always thermodynamically unstable. In this work, we revisit the thermodynamic stability of ultraspinning black holes by performing a systematic analysis of the heat capacity in different ensembles over the full range of the horizon radius $r_H$, which were missed in earlier temperature-based analyses. We demonstrate for the first time that, contrary to earlier claims, ultraspinning black holes can admit thermodynamically stable regions, whose existence crucially depends on the spacetime dimension, the solution branch, and the presence of charge. In addition, we present the first application of the revised reverse isoperimetric inequality to ultraspinning black holes. Despite the violation of the original reverse isoperimetric inequality in this super-entropic regime, we find that the revised inequality remains applicable and imposes nontrivial constraints on the allowed parameter space, including an upper bound on the ultraspinning parameter $\mu$, strengthened lower bounds on the mass $m$, and upper bounds on both the charge $q$ and the AdS radius $l$. To ensure the consistency of the thermodynamic description, the conserved charges and the first law in the ultraspinning limit are derived using the Iyer-Wald formalism together with integrability conditions.