Thermodynamics of black holes and self-gravitating hot matter

Abstract:

Black holes and self-gravitating hot matter can be viewed as thermodynamic objects. This fact reveals the existence of a link between thermodynamics and gravitation, since at a fundamental level thermodynamics stems from the quantum behavior of the systems. The essence of the connection is still unknown, but it is indicated that comes from the quantum character of gravitation. To shed light on the nature of this link, it is essential to analyze the thermodynamic properties of curved spacetime with black holes and self-gravitating matter together.

It is also interesting to generalize the analysis to higher dimensions, in connection with theories of quantum gravity that require dimensions higher than four. In this seminar, I will mainly focus on two works: I will present the thermodynamic properties of a charged spherical hot thin shell in higher dimensions, by imposing the first law of thermodynamics, showing its entropy and its thermodynamic stability, where suggestive equations of state have been chosen for the shell, clarifying thus the contributions of the self-gravitating nature of ordinary matter to the entropy and other thermodynamic quantities; I will also present the grand canonical ensemble of a d-dimensional charged black hole in a cavity, through the Euclidean path integral approach in the zero loop approximation, which has two solutions for the horizon radius of the black hole, where the solution with the largest radius is stable.

In addition, I will present the ongoing work on the canonical ensemble of charged black holes in acavity, the canonical ensemble for pure self-gravitating hot matter shells, and the grand canonical ensemble of black holes and matter shells, as well as other recent projects.