Thermodynamical description of stationary, asymptotically flat solutions with conical singularities

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.Comment: 19 pages, 12 figure

Thermodynamic potentials and Thermodynamic Relations in Nonextensive Thermodynamics

The generalized Gibbs free energy and enthalpy is derived in the framework of nonextensive thermodynamics by using the so-called physical temperature and the physical pressure. Some thermodynamical relations are studied by considering the difference between the physical temperature and the inverse of Lagrange multiplier. The thermodynamical relation between the heat capacities at a constant volume and at a constant pressure is obtained using the generalized thermodynamical potential, which is found to be different from the traditional one in Gibbs thermodynamics. But, the expressions for the heat capacities using the generalized thermodynamical potentials are unchanged.Comment: 7 page

On the thermodynamical limit of self-gravitating systems

It is shown that the diluted thermodynamical limit of a self-gravitating system proposed by de Vega and Sanchez suffers from the same problems as the usual thermodynamical limit and leads to divergent thermodynamical functions. This question is also discussed from the point of view of mean field theory.Comment: 11 pages. A typo corrected. Cosmetic changes in some equations. Version that appear in the journa

Nonextensive Thermostatistical Investigation of The Blackbody Radiation

Thermodynamical quantities of the blackbody radiation, such as free energy, entropy, total radiation energy, specific heat are calculated within the Tsallis thermostatistics where factorization method is incorparated. It is shown that basic thermodynamical relation of the blackbody radiation is form invariant with respect to nonextensivity entropic index q. Furthermore, the nonextensive thermodynamical quantities related to the blackbody radiation is seperately be obtained in terms of q and the standard thermodynamical quantities of the blackbody radiation .It is indicated that the formulation may give a way to determine the q which determines the degree of the nonextensivity that is the one of the aims of the present study.Comment: 16 pages,No figures,to be appear in Chaos,Solitons&Fractal

On Thermodynamics of AdS Black Holes in M-Theory

Motivated by a recent work on asymptotically AdS_4 black holes in M-theory, we investigate the thermodynamics and thermodynamical geometry of AdS black holes from M2 and M5-branes. Concretely, we consider AdS black holes in AdS_{p+2}\times S^{11-p-2}, where p=2,5 by interpreting the number of M2 (and M5-branes) as a thermodynamical variable. We study the corresponding phase transition to examine their stabilities by calculating and discussing various thermodynamical quantities including the chemical potential. Then, we compute the thermodynamical curvatures from the Quevedo metric for M2 and M5-branes geometries to reconsider the stability of such black objects. The Quevedo metric singularities recover similar stability results provided by the phase transition program.Comment: 16 pages, 12 figures. Late