Thermodynamics and statistical mechanical ensembles of black holes and self-gravitating matter

TL;DR

This thesis explores the thermodynamics of black holes and self-gravitating matter, using statistical ensembles and the first law of thermodynamics to understand phase transitions and microstates at the microscale.

Contribution

It introduces a novel approach combining the first law and Euclidean path integrals to analyze black hole thermodynamics and phase transitions in various spacetime settings.

Findings

Demonstrates the thermodynamic properties of charged black holes in different ensembles.

Shows phase transitions between hot matter and black hole states.

Provides insights into the microstates underlying black hole entropy.

Abstract

Black holes exist all over our Universe, possessing a very wide range of masses. At the moment, they serve as a probe to test general relativity at astrophysical scales, but in the future they may also give us information about gravity at the microscale. Black holes seem to have thermodynamic properties, such as the Bekenstein-Hawking entropy, which are important when considering black holes with size of a few centimeters or smaller. Since entropy in statistical mechanics is related to the number of microstates of a system, several questions arise: what gives rise to the black hole entropy? Can it be explained by a quantum description of gravity? In order to further study these questions, the connection between thermodynamics and gravity must be explored at the microscale. In this doctoral thesis, we aim to understand this connection using two descrip-tions that yield the thermodynamics of curved spacetimes. We start by imposing the first law of thermodynamics to a charged self-gravitating matter thin shell in higher dimensions and choose equations of state which allow the study of the black hole limit and the recovery of black hole thermodynamics. Furthermore, we use the Euclidean path integral approach to quantum gravity to construct statistical ensembles of black hole spacetimes and self-gravitating matter, in order to study semiclassically the phase transitions between hot matter and black holes. We show the power of the formalism in obtaining the thermodynamic properties of curved spacetimes. Namely, we study the canonical and grand canonical ensemble of charged black holes inside a cavity, which may have a finite or infinite radius. We construct ensembles of a self-gravitating matter thin shell, both in anti-de Sitter and in asymptotically flat spaces, in order to understand the thermodynamic features of the shell and the possible phase transitions to black hole configurations.