Thermodynamics of two aligned Kerr black holes

TL;DR

This paper explores the thermodynamics of two Kerr black holes in stationary equilibrium, deriving a relation for the thermodynamic length based on the double-Kerr solution and extending thermodynamic principles to binary black hole systems.

Contribution

It introduces a novel formulation of the thermodynamic length for binary Kerr black holes, linking it to the metric function and the strut's coordinate length, expanding understanding of black hole thermodynamics.

Findings

Thermodynamic length is given by $ ext{L} imes ext{exp}( ext{γ}_0)$.

The analysis extends thermodynamic laws to binary Kerr black hole configurations.

The study connects the thermodynamics of stationary binary systems with the extended double-Kerr solution.

Abstract

We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $\ell$ is defined by the formula $\ell=L\exp(\gamma_0)$, where $L$ is the coordinate length of the strut, and $\gamma_0$ is the value of the metric function $\gamma$ on the strut.