Thermodynamics and Phase Transitions of Black Holes - Jimenez, Andres Felipe Cardona (2020)
In this thesis we study aspects of thermodynamics, field dynamics and phase transitions of non-asymptotically flat black holes that are important in the context of gauge/gravity dualities. In Anti-de Sitter geometries the processes of black hole evaporation and phase transitions are characterized. We consider the Vaidya Anti-de Sitter spacetime as a model for evaporation or gravitational collapse, in which a time dependency is introduced by means of a mass function evolving in time. For the study of thermodynamics of black holes evolving in time we follow a formalism adapted to non-stationary spacetimes with thermodynamical quantities associated to geometric properties of the so called trapping horizons. For Anti-de Sitter geometries we compare the thermodynamical results with the corresponding dual gauge theory established in the AdS/CFT correspondence. It is also considered the field dynamics of certain geometries where perturbative results can be associated with a symmetry group not associated to the isometries of the background spacetime.