On the thermodynamic stability of rotating black holes in higher dimensions -- a comparison of thermodynamic ensembles

Understand

Thermodynamic potentials relevant to the micro-canonical, the canonical and the grand-canonical ensembles, associated with rotating black holes in D-dimensions, are analysed and compared.

• Such black holes are known to be thermodynamically unstable, but the instability is a consequence of a subtle interplay between specific heats and the moments of inertia and it manifests itself differently in the different ensembles.
• A simple relation between the product of the specific heat and the determinant of the moment of inertia in both the canonical and the grand-canonical ensembles is derived.
• Myers-Perry black holes in arbitrary dimension are studied in detail.