Black hole superradiant instability for massive spin-2 fields
Óscar J. C. Dias, Giuseppe Lingetti, Paolo Pani, Jorge E. Santos
Abstract
Because of coherent superradiant amplification, massive bosonic fields can trigger an instability in spinning black holes, tapping their energy and angular momentum and forming macroscopic Bose-Einstein condensates around them. This phenomenon produces gaps in the mass-spin distribution of astrophysical black holes, a continuous gravitational-wave signal emitted by the condensate, and several environmental effects relevant for gravitational-wave astronomy and radio images of black holes. While the spectrum of superradiantly unstable mode is known in great detail for massive scalar (spin-0) and vector (spin-1) perturbations, so far only approximated results were derived for the case of massive tensor (spin-2) fields, due to the nonseparability of the field equations. Here, solving a system of ten elliptic partial differential equations, we close this program and compute the spectrum of the most unstable modes of a massive spin-2 field for generic black-hole spin and boson mass, beyond the hydrogenic approximation and including the unique dipole mode that dominates the instability in the spin-2 case. We find that the instability timescale for this mode is orders of magnitude shorter than for any other superradiant mode, yielding much stronger constraints on massive spin-2 fields. These results pave the way for phenomenological studies aimed at constraining beyond Standard Model scenarios, ultralight dark matter candidates, and extensions to general relativity using gravitational-wave and electromagnetic observations, and have implications for the phase diagram of vacuum solutions of higher-dimensional gravity.