Thermodynamics of two aligned Kerr-Newman black holes

TL;DR

This paper derives the thermodynamic laws for two aligned Kerr-Newman black holes connected by a strut, introducing a simple formula for thermodynamic length and proposing an expression for free energy.

Contribution

It provides a novel derivation of thermodynamic relations for binary Kerr-Newman black holes using thermodynamic length and offers an analytic formula for this length.

Findings

Thermodynamic length is given by a simple exponential formula.

First law of thermodynamics is consistently derived for the system.

An expression for the free energy of two Kerr-Newman black holes is proposed.

Abstract

Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. Like in the electrostatic systems of two Reissner-Nordstr\"om black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $\ell$ turns out to be defined by the same simple formula $\ell=L\exp(\gamma_0)$, $L$ being the coordinate length of the strut and $\gamma_0$ the value of the metric function $\gamma$ on the strut, which permits the elaboration of $\ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.