Penrose process, superradiance, and ergoregion instabilities

Superradiant scattering is a radiation enhancement process that takes place in many contexts, and which has recently found exciting applications in astrophysics and particle physics. In the framework of curved spacetime physics, it has been associated with the classical Penrose process for particles. Superradiance is usually also associated with bosonic fields around geometries with ergoregions and horizons. These notions are in clear tension however: the Penrose process occurs for horizonless geometries, and particles are composed of fermions. Here, we resolve the tension in its different aspects, by showing that (i) superradiance occurs for self-interacting fermions on flat spacetime. (ii) Superradiance occurs also for horizonless geometries, where it leads to an ergoregion instability. Ultracompact, horizonless geometries will usually respond with echoes of growing amplitude, until rotational (or electrostatic) energy is extracted from the object. (iii) The Fourier-domain analysis leads to absence of superradiance when horizons are not present. We elucidate why this analysis fails to give meaningful results. (iv) Finally, we show that superradiant, ergoregion instabilities have a particle analog of similar growth timescales and which can power the formation of a structure outside a compact, rotating star.