Nonsingular and deformed black holes Fundamental aspects and phenomenology

Einstein’s theory of gravity, general relativity, stands as one of the most successful and enduring pillars of modern physics. Its predictions have consistently aligned with a vast array of observed phenomena within our Universe. However, the enigmatic nature of gravity persists, particularly when examined at both extremely short and exceedingly vast distances. In this thesis, we explore several aspects of black hole physics, which could encode ignatures of quantum gravity effects at different, even macroscopic, scales. We will investigate modifications and deformations of classical black-hole geometries in a model-independent manner. We start by deriving a general class of regular black holes sourced by an anisotropic fluid violating the strong energy condition and allowing for the circumvention of Penrose’s theorems. The anisotropies are then assumed to parameterize some quantum effects, whose typical scale is encoded in an additional quantum parameter (hair) ℓ. We then turn our attention to the thermodynamics of these models, revealing a preference for the states with ℓ of the order of the horizon scale. This aspect is further investigated through theanalysis of semiclassical dynamics, i.e., the Hawking evaporation process, by using a simple two dimensional balck-hole model. We also test these models against orbits of stars around our galactic center, placing constraints on the strength of the quantum effects. In a separate developement, we study a general class of deformed, rotating, singular black holes, focusing on their phenomenology and, in particular, the superradiant amplification of test fields. We then consider the problem of describing the gravitational field generated by a quantum particle in a delocalized state. The resultant geometry resembles the first models we analyzed, allowing to reinterpret the smearing of the singularity in terms of the uncertainty principle. Finally, we analyze a model in which black holes are medelled as sets of oscillators whose typical frequencies are given by the quasinormal modes of the systems. Under some assumptions,we are able to obtain the Bekenstein-Hawking formula for the entropy and its first, logarithmic correction. Finally, we reinterpret this model in terms of the dual conformal field theory at the boundary, finding that the perturbations of two-dimensional regular black holes are related to a conformally-invariant generalization of the quantum harmonic oscillator, described by the de Alfaro-Fubini-Furlan theory.