Thermodynamical description of stationary, asymptotically flat solutions with conical singularities

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 [1]. 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 BekensteinHawking 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.

Charged dilatonic black rings and black saturns and their thermodynamics

“…Here the relations for the charged dilatonic black saturn and the relations for the neutral black saturn are the same (see [37]). As in [37] figure 7 shows the parameter space of the charged dilatonic black saturn.…”

“…As in [37] figure 7 shows the parameter space of the charged dilatonic black saturn. In the coloured region the charged dilatonic black saturn is in thermodynamical equilibrium.…”

“…Clearly, in equilibrium the Hawking temperature of both objects has to be the same. In addition both objects should have the same angular velocity (see [37], [38]) and the same horizon electrostatic potential. The latter is already fulfilled, so one just needs to consider…”

“…In a (stationary and asymptotically flat) spacetime that contains a conical singularity, the first law of thermodynamics gets an extra term AdP (see [36], [37]). P is the pressure caused by the conical singularity and A/T H is the area spanned by the conical singularity.…”

“…To analyse the thermodynamical stability two quantities are considered (compare [37]), the specific heat at constant angular momentum…”