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Thermodynamical description of stationary, asymptotically flat solutions with conical singularities

2010; American Physical Society; Volume: 81; Issue: 10 Linguagem: Inglês

10.1103/physrevd.81.104031

1550-7998

Carlos Herdeiro, Eugen Radu, Carmen Rebelo,

Quantum Electrodynamics and Casimir Effect

We examine the thermodynamical properties of a number of asymptotically flat, stationary (but not static) solutions having conical singularities, with both connected and nonconnected event horizons, using the thermodynamical description recently proposed in [C. Herdeiro, B. Kleihaus, J. Kunz, and E. Radu, Phys. Rev. D 81, 064013 (2010).]. 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 Arnowitt-Deser-Misner angular momentum. We also analyze 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.