Dynamical models and extended thermodynamics for black holes with cosmological constant - Campos, Thiago de Lima (2025)
In this thesis, black holes in settings involving a cosmological constant are investigated, emphasizing their thermodynamic characteristics. The research is structured into two related but distinct parts, each addressing an important aspect of the investigation. In the first part of the thesis, dynamical processes involving black holes are modeled using Haywards thermodynamic framework. Vaidya-de Sitter spacetime is used to study the evaporation of a black hole in a scenario of accelerated expansion. It is found that timescale of evaporation strongly depends on the cosmological observer. Considering accretion mechanisms around the compact objects, we propose a systematic perturbative scheme for the Misner-Sharp mass in the neighborhood of an arbitrary future trapping horizon. In this context, we develop approximations in the form of Vaidya-dark energy. The results show how energy flux and density affect the position of the perturbed horizon in distinct ways. In the second part of the thesis, we study the construction of different thermodynamic descriptions for Kerr-anti-de Sitter (Kerr-adS) black holes. Isohomogeneous transformations, a procedure for generating new thermodynamics, are presented and interpreted geometrically within the Iyer-Wald formalism. In this new framework, the usual Kerr-adS thermodynamics is complemented by its geometric construction, and Hawkings proposal, which does not satisfy a first law, is improved into an alternative thermodynamic theory. Using a Euclidean approach, we propose an interpretation of the different thermodynamic representations in terms of frame and gauge choices. This thesis provides new insights into the role of a cosmological constant in shaping the dynamical evolution and thermodynamic properties of black holes