Applications of perturbation theory in black hole physics

Black holes have many faces. Arguably, they are the most interesting objects in theoretical physics, revealing the elusive connection between gravity and quantum mechanics. Within the gauge/string duality they provide useful insights on strongly coupled quantum field theories and on quantum gravity. Furthermore, probing the strong curvature regime of any gravity theory, black holes carry the imprint of possible strong curvature corrections to General Relativity. Finally, beside their unique theoretical properties, several experimental evidences suggest that astrophysical black holes exist in nature and they are believed to be very common objects in the universe. In this dissertation we discuss several applications of linear perturbation theory in black hole physics. As applications in theoretical physics, we study perturbations of dilatonic black holes in Einstein-Maxwell theory and the holographic properties of the dual field theory via the Anti de Sitter/Condensed Matter duality. Furthermore we discuss a method to compute long-lived quasinormal modes of Schwarzschild-Anti de Sitter black holes and we study vortex black hole solutions in three dimensional Anti de Sitter gravity. As applications in astrophysics, we discuss how the characteristic oscillations of black holes in string-inspired theories of gravity can provide observable signatures of deviations from General Relativity. We study two well-motivated effective theories: Dynamical Chern-Simons gravity and Einstein-Dilatonic-Gauss-Bonnet gravity. We conclude by discussing the black hole paradigm. Motivated by the lacking of a definitive answer on the existence of astrophysical black holes, we study some viable alternatives, generally called “black hole mimickers”. We focus on two representative cases: static thin-shell gravastars and superspinars. We discuss their stability, gravitational-wave signature and viability as astrophysical objects.