Thermodynamics of nonextremal Kaluza-Klein multiblack holes in five dimensions

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.

Double-black-hole solutions of the Einstein-Maxwell-dilaton theory in five dimensions

“…In order to construct multi-black hole configurations in spaces with Kaluza-Klein asymptotics it turns out that one has to modify this solution-generating technique as in [41]. The double-Reissner-Nordström solution in this background has been constructed in [41], while more general solutions with Kaluza-Klein asymptotics have been derived in [42]. Finally, solutions describing charged black holes on the Taub-bolt instanton have been studied in [43], [44], while charged multi-black holes on Kaluza-Klein bubbles have been derived in [45].…”

“…See for instance the solution with c = 0 in equation (39) in[42], which was based on the general Harisson transformation in[51].…”