Black holes beyond general relativity: theoretical and phenomenological developments.

In four dimensions, general relativity is the only viable theory of gravity satisfying the requirements of diffeoinvariance and strong equivalence principle. Despite this aesthetic appeal, there are theoretical and experimental reasons to extend gravity beyond GR. The most promising tests and bounds are expected to come from strong gravity observations. The past few years have seen the rise of gravitational wave astronomy, which has paved the way for strong gravity observations. Future GW observations from the mergers of compact objects will be able to constrain much better possible deviations from GR. Therefore, an extensive study of compact objects in modified theories of gravitation goes in parallel with these experimental efforts. In this PhD Thesis we concentrate on black holes. Black holes act as testbeds for modifications of gravity in several ways. While in GR they are extremely simple objects, in modified theories their properties can be more complex, and in particular they can have hair. The presence of hair changes the geometry felt by test fields and it modifies the generation of GW signals. Moreover, black holes are the systems in which the presence of singularities is predicted by classical gravity with the highest level of confidence: this is not only true in GR, but also in most of the modified gravity theories formulated in classical terms as effective field theories. Singularities are regarded as classical artifacts to be cured by quantum gravity effects. Therefore, considering mechanisms of singularity resolutions is a theoretical arena to study the form of these effects. The Thesis presents theoretical contributions to all these aspects of black hole physics. The work is organized following three main topics: black holes with universal horizons, hairy black holes in Einstein-Maxwell-dilaton theory and regular black holes. These models originate from various motivations: black holes with universal horizons are found in modified gravity theories which break local Lorentz symmetry; Einstein-Maxwell-dilaton black holes originate in string theory and in lower dimensional compactifications, but they also serve as proxies for black holes in theories propagating additional degrees of freedom; regular black holes are motivated by the efforts to understand how quantum gravity solves the classical singularities. In each of the above cases, we present results which appear to be relevant for the follow up research in their respective fields. We also emphasize that, besides the contextual significance of our results, we also developed thechniques for addressing the respective problems, which can be useful well beyond the specific cases considered in this Thesis.