Aspects of Quantum Field Theory in curved spacetime

This doctoral thesis explores the intersection of Quantum Field Theory and General Relativity within the framework of Quantum Field Theory in curved spacetimes. The research is divided into two primary sections: the development of mathematical tools regarding the effective action and heat kernel methods, and the application of these tools to two-dimensional black hole models. In the first part, we address the definition and calculation of the 1-loop effective action, a crucial object for studying quantum corrections to classical field theories. While the standard Gilkey-Seeley-DeWitt expansion provides a method for regularizing divergencies, it is computationally costly and perturbative in nature. This document presents and expands upon a resummation scheme for the heat kernel that captures some non-perturbative information and simplifies the calculation of the leading order terms. This resummation formula is successfully applied to various systems, including scalar fields with Yukawa couplings, Quantum Electrodynamics, and inhomogeneous field configurations. These methods allow for a more precise analysis of phenomena such as the Schwinger effect and vacuum polarization. The second part focuses on the semiclassical evolution of black holes, utilizing 2D dilaton gravity models (specifically the Callan-Giddings-Harvey-Strominger model) as a testing ground to address conceptual issues like information loss and spacetime singularities. We examine the Russo-Susskind-Thorlacius model, which solves the backreaction equations but typically predicts the formation of naked singularities, threatening the unitarity of the theory. To resolve these issues, we propose a modification to the standard semiclassical approach by incorporating fields with negative central charges (such as Faddeev-Popov ghosts) coupled to an auxiliary conformally flat metric. The results demonstrate that, under specific conditions involving sufficiently large negative central charges, the naked singularity is removed entirely from the spacetime evolution. Instead, the system evolves with an apparent horizon that hides a regular region of spacetime, suggesting a pathway for black hole evolution that avoids catastrophic breakdowns of predictability and offers new perspectives on the role of matter content in gravitational collapse.