Modern topics in black hole physics and cosmology

Motivated by the new opportunities that gravitational wave detections of-fer in both cosmology and astrophysics, in this thesis we study potentially detectable physical phenomena related with black hole physics, with partic-ular interest to systems of black holes interacting with cosmological scalar fields.First of all, we study a charged, rotating black hole solution in a Gener-alised Proca theory of gravity, obtained through a disformal transformation of the Einstein-Maxwell action. Due to the breaking of gauge symmetry, the gauge freedom of the components of the gauge vector is lost; thus, for a particular choice of the gauge vector, we are able to find an exact, charged, rotating black hole solution, with event horizon and ergosphere parametri-cally different from the General Relativity solution. For such solution, the Innermost Stable Circular Orbits (ISCOs) are studied. Subsequently, we consider the effects of an external, ultralight scalar field interacting with an electromagnetic Kerr-Newman black hole. Depending on the frequen-cies of the scalar’s modes and on the angular velocity of the black hole, the scalar waves scattering off the event horizon may trigger superradiance; for some scalar field’s modes, a stationary scalar cloud is developed in the black hole’s surroundings, and the frequencies of the scalar’s modes in the cloud correspond to the resonant frequencies of the superradiant gain fac-tor. Moreover, we investigate the effects of a massless scalar field coupled to an electromagnetic rotating black hole through Chern-Simons couplings; in particular, we consider both scalar-vector and scalar-tensor couplings. Us-ing both a slow rotation and small couplings approximation scheme, we are able to find an hairy black hole solution up to second order in the approxi-mation parameters. Such solution carries a secondary scalar charge, and it satisfies the Smarr formula for black hole thermodynamics. Furthermore, we propose a possible revealing effect for such hairy configuration, based on the polarization dependent angular deflection to which photons are subject to when interacting with the scalar field. At the end, we study the linear perturbation theory for a static, electromagnetic black hole, also including a Chern-Simons scalar-vector coupling to an external, massless axion field. We find that due to the presence of the magnetic charge the decoupling be-tween axial and polar perturbations is broken, leading to a Regge-Wheeler perturbation equation containing terms with different parity.