Into the Heart of Darkness: Theory and Phenomenology of Regular Black Holes

Spacetime singularities are a generic prediction of general relativity. They are believed to mark the breakdown of the theory and, for this reason, they represent one of the main drivers for the search for alternative theories of gravity; in particular, it is commonly expected that the formation of singularities will be prevented in a full theory of quantum gravity. In this view, it is reasonable to assume that non-singular — or regular — metrics can provide an effective description of the outcome of gravitational collapse and a credible alternative to general-relativistic black holes. In this thesis, we explore such hypothesis by providing strategies for constructing regular geometries of various kinds: simply and multiply connected, with and without horizons — thus exhausting all of the qualitatively different alternatives. The approach is largely theory-agnostic, with particular emphasis being placed on rotating models. Ample room is devoted to a specific family of regular geometries known as black bounces. They represent wormholes that may or may not exhibit horizons, depending on the value of one parameter. The thesis describes the construction of the black-bounce counterparts to the Kerr and Kerr–Newman geometries; scalar test-field perturbations to one of these metrics are then examined by computing the quasi-normal modes and the superradiant amplification factors. The discussion is then specialised to the context of a compelling candidate quantum theory of gravity: non-projectable Hořava gravity. In particular, regular black holes and horizonless ultra-compact objects are constructed under the assumption of staticity and spherical symmetry, and analysed through the lenses of the theory’s low-energy limit. In preparation to the addition of rotation, a Kerr black hole solution is then examined in the closely related Einstein–æther theory. This thesis thus contributes to the investigation of alternative descriptions for astrophysical black holes beyond general relativity, particularly with regards to regular black holes and horizonless black-hole mimickers. Therefore, it naturally aligns with the research programme of quantum gravity phenomenology.