Superradiant instabilities of black holes

Abstract: Rapidly-spinning black holes can actually *increase* their event horizon area, and hence their entropy, by shedding mass and angular momentum. This thermodynamic statement underpins various energy-extraction mechanisms, such as the Penrose process, or the stimulated emission of radiation known as superradiance. If, by some mechanism, superradiance is reflected back onto a black hole, an instability may be generated. In particular, for bosonic fields with rest mass, certain gravitationally-bound states of the field (analogous to electron orbitals in hydrogen) become linearly unstable. I will describe some recent work on quantifying the instability, and assessing its possible astrophysical relevance.