A note on the entropy of charged multi - black - holes

TL;DR

This paper investigates the entropy of charged multi-black-hole solutions in Einstein-Maxwell theory, demonstrating that under certain boundary conditions, the Euclidean action indicates zero entropy for these configurations.

Contribution

It provides a novel analysis of the entropy of multi-black-hole solutions, showing that they have zero entropy in the canonical ensemble, which contrasts with typical black hole thermodynamics.

Findings

Multi-black-hole solutions have zero entropy under canonical boundary conditions.

The Euclidean action approach confirms the zero entropy result.

The study extends to higher dimensions, maintaining the zero entropy conclusion.

Abstract

Majumdar--Papapetrou multi--black-hole solutions of the Einstein--Maxwell equations are considered in four and higher dimensions. The Euclidean action with boundary conditions appropriate to the canonical ensemble is shown to lead to zero entropy.