Multi-black hole configurations on the cylinder

TL;DR

This paper constructs and analyzes new multi-black hole solutions on a cylindrical space, revealing implications for black hole phase structure, non-uniqueness, and potential new black string and black hole configurations.

Contribution

It introduces first-order multi-black hole solutions on a cylinder and explores their thermodynamics, equilibrium conditions, and implications for black hole phase diagrams and non-uniform strings.

Findings

Multi-black hole solutions valid at small total mass

Continuous non-uniqueness in the phase diagram of Kaluza-Klein black holes

Potential existence of new non-uniform and lumpy black hole solutions

Abstract

We construct the metric of new multi-black hole configurations on a d-dimensional cylinder R^{d-1} x S^1, in the limit of small total mass (or equivalently in the limit of a large cylinder). These solutions are valid to first order in the total mass and describe configurations with several small black holes located at different points along the circle direction of the cylinder. We explain that a static configuration of black holes is required to be in equilibrium such that the external force on each black hole is zero, and we examine the resulting conditions. The first-order corrected thermodynamics of the solutions is obtained and a Newtonian interpretation of it is given. We then study the consequences of the multi-black hole configurations for the phase structure of static Kaluza-Klein black holes and show that our new solutions imply continuous non-uniqueness in the phase diagram. The new multi-black hole configurations raise the question of existence of new non-uniform black strings. Finally, a further analysis of the three-black hole configuration suggests the possibility of a new class of static lumpy black holes in Kaluza-Klein space.