Many accelerating distorted black holes

TL;DR

This paper constructs an analytical solution in General Relativity for multiple accelerating black holes, showing they can be in equilibrium without external struts, and explores their thermodynamics and special cases.

Contribution

It introduces a regularized multi-black hole solution with acceleration in GR, avoiding conical singularities via external fields, and analyzes its thermodynamic properties.

Findings

Black hole arrays can be in equilibrium without struts.

The solution includes special cases like accelerating Schwarzschild and double C-metric.

Thermodynamics of these black holes are consistent with Smarr law.

Abstract

An analytical metric of four-dimensional General Relativity, representing an array of collinear and accelerating black holes, is constructed with the inverse scattering method. The solution can be completely regularised from any conical singularity, thanks to the presence of an external gravitational field. Therefore the multi-black hole configuration can be maintained at equilibrium without the need of string or struts. Some notable subcases such as the accelerating distorted Schwarzschild black hole and the double distorted C-metric are explicitly presented. The Smarr law and the thermodynamics of these systems is studied. The Bonnor-Swaminarayan and the Bi\v{c}\'ak-Hoenselaers-Schmidt particle metrics are recovered, through appropriate limits, from the multi-black holes solutions.