Thermodynamics of Many Black Holes

TL;DR

This paper explores the thermodynamics of multiple black holes, including accelerating ones, establishing a general First Law and analyzing specific cases like the C-metric, thereby extending black hole thermodynamics theory.

Contribution

It introduces a general First Law for collinear black holes with varying tensions, including accelerating black holes, and relates it to known solutions like the C-metric.

Findings

Proved a general First Law including tension variations.

Established the robustness of the thermodynamic length concept.

Derived a Christoudoulou-Ruffini formula for the C-metric.

Abstract

We discuss the thermodynamics of an array of collinear black holes which may be accelerating. We prove a general First Law, including variations in the tensions of strings linking and accelerating the black holes. We analyse the implications of the First Law in a number of instructive cases, including that of the C-metric, and relate our findings to the previously obtained thermodynamics of slowly accelerating black holes in anti-de Sitter spacetime. The concept of thermodynamic length is found to be robust and a Christoudoulou-Ruffini formula for the C-metric is shown.