Thermodynamical description of stationary, asymptotically flat solutions with conical singularities

TL;DR

This paper investigates the thermodynamics of various asymptotically flat, stationary solutions with conical singularities, confirming the Bekenstein-Hawking law and analyzing their stability, finding all are thermodynamically unstable.

Contribution

It applies a recent thermodynamical framework to complex solutions like double-Kerr and black rings, confirming key laws and analyzing stability.

Findings

Bekenstein-Hawking area law is recovered

Thermodynamical angular momentum equals ADM angular momentum

All solutions are thermodynamically unstable

Abstract

We examine the thermodynamical properties of a number of asymptotically flat, stationary (but not static) solutions having conical singularities, with both connected and non-connected event horizons, using the thermodynamical description recently proposed in arXiv:0912.3386 [gr-qc]. The examples considered are the double-Kerr solution, the black ring rotating in either S^2 or S^1 and the black Saturn, where the balance condition is not imposed for the latter two solutions. We show that not only the Bekenstein-Hawking area law is recovered from the thermodynamical description but also the thermodynamical angular momentum is the ADM angular momentum. We also analyse the thermodynamical stability and show that, for all these solutions, either the isothermal moment of inertia or the specific heat at constant angular momentum is negative, at any point in parameter space. Therefore, all these solutions are thermodynamically unstable in the grand canonical ensemble.