Thermodynamics for higher dimensional rotating black holes with variable Newton constant

TL;DR

This paper analytically proves the extensivity of thermodynamics for higher-dimensional rotating black holes with a variable Newton constant, providing explicit formulas and analyzing their stability.

Contribution

It introduces a framework for thermodynamics with variable G, deriving explicit macro state functions for Myers-Perry black holes and analyzing their stability.

Findings

Myers-Perry black holes are thermodynamically unstable.

Explicit macro state functions are derived for these black holes.

The framework applies to black holes with or without cosmological constant.

Abstract

The extensivity for the thermodynamics of general $D$-dimensional rotating black holes with or without a cosmological constant can be proved analytically, provided the effective number of microscopic degrees of freedom and the chemical potential are given respectively as $N=L^{D-2}/G, \mu= GTI_D/L^{D-2}$, where $G$ is the variable Newton constant, $I_D$ is the Euclidean action and $L$ is a constant length scale. In the cases without a cosmological constant, i.e. the Myers-Perry black holes, the physical mass and the intensive variables can be expressed as explicit macro state functions in the extensive variables in a simple and compact form, which allows for an analytical calculation for the heat capacity. The results indicate that the Myers-Perry black holes with zero, one and $k$ equal rotation parameters are all thermodynamically unstable.