Thermodynamics of two black holes

TL;DR

This paper analyzes the thermodynamics of a system of two charged black holes connected by a strut, deriving explicit formulas for thermodynamic parameters and introducing the concept of thermodynamical length.

Contribution

It introduces a novel thermodynamic framework for two black holes with a strut, including explicit formulas for thermodynamic parameters and the concept of thermodynamical length.

Findings

Derived explicit thermodynamic parameters for the black hole system.

Formulated a consistent first law of thermodynamics for the system.

Introduced the concept of thermodynamical length related to the strut.

Abstract

We study a system of two charged non-rotating black holes separated by a strut. Using the exact solution of the Einstein-Maxwell equations, which describes this system, we construct a consistent form of the first law of thermodynamics. We derive thermodynamic parameters related to the strut in an explicit form. The intensive thermodynamical quantity associated with the strut is its tension. We call the corresponding extensive quantity the thermodynamical length and we provide an explicit expression and interpretation for it.