On explicit thermodynamic functions and extremal limits of Myers-Perry black holes

TL;DR

This paper derives explicit thermodynamic relations for Myers-Perry black holes in arbitrary dimensions, analyzes their extremal limits, and visualizes their thermodynamic geometry as a wedge in Minkowski space.

Contribution

It provides explicit fundamental thermodynamic relations and geometric representations for Myers-Perry black holes across arbitrary dimensions, including extremal bounds.

Findings

Derived explicit temperature and heat capacity formulas.

Established the generalized Kerr bound in arbitrary dimensions.

Represented thermodynamic state space as a wedge in Minkowski space.

Abstract

We study thermodynamic properties of Myers-Perry black holes by deriving explicit fundamental relations from which we can obtain the temperature and specific heat in terms of explicit control parameters in arbitrary dimensions. Using the definition of extremal black holes we establish the generalized Kerr bound in arbitrary dimension. We study thermodynamic geometries of the Myers-Perry black holes with equal angular momenta in arbitrary dimensions and draw thermodynamic cone diagrams which capture the extremal limits of the black holes. Thermodynamic state space is represented geometrically as a wedge embedded in Minkowski space. The opening angle of such a wedge is uniquely determined by the number of spacetime dimensions and the number of angular momenta. Our results can potentially be used to generalize thermodynamic instability analysis and other studies in which extremal limits of the Myers-Perry black holes are required.