Abstract: Superradiance is a radiation enhancement process that involves dissipative systems. In General Relativity, black-hole superradiance is permitted by dissipation at the event horizon that allows for energy and angular momentum extraction from the vacuum, even at the classical level. Various mechanisms (as diverse as massive fields, magnetic fields, anti-de Sitter boundaries, nonlinear interactions, etc...) can confine the amplified radiation and give rise to strong instabilities.
In this talk I will give a unified treatment of the subject. In particular I will show how magnetic fields can confine radiation and trigger superradiant instabilities, performing the first fully-consistent linear analysis of the Ernst spacetime, an exact solution of the Einstein-Maxwell equations describing a black hole immersed in a uniform magnetic field. Finally I will discuss the astrophysical implications of our results.