Thermodynamics of non-extremal Kaluza-Klein multi-black holes in five dimensions

TL;DR

This paper derives and analyzes the thermodynamics of multi-black hole solutions in five-dimensional Kaluza-Klein spacetime, revealing that entropy obeys the Bekenstein-Hawking law despite conical singularities.

Contribution

It introduces a new exact solution for non-extremal multi-black holes with Kaluza-Klein asymptotics and extends thermodynamic laws to these configurations with singularities.

Findings

Entropy follows Bekenstein-Hawking law in Kaluza-Klein spaces

Solutions exhibit conical singularities that cannot be fully eliminated

Charged generalization and extremal limit are obtained

Abstract

Using a solution-generating method, we derive an exact solution of the Einstein's field equations in five dimensions describing multi-black hole configurations. More specifically, this solution describes systems of non-extremal static black holes with Kaluza-Klein asymptotics. As expected, we find that, in general, there are conical singularities in-between the Kaluza-Klein black holes that cannot be completely eliminated. Notwithstanding the presence of these conical singularities, such solutions still exhibit interesting thermodynamical properties. By choosing an appropriate set of thermodynamic variables we show that the entropy of these objects still obeys the Bekenstein-Hawking law for spaces with Kaluza-Klein asymptotics. This extends the previously known thermodynamic description of asymptotically flat spaces with conical singularities to general spaces with Kaluza-Klein asymptotics with conical singularities. Finally, we obtain a charged generalization of this multi-black hole solution in the general Einstein-Maxwell-Dilaton theory and show how to recover the extremal multi-black hole solution as a particular case.