# Superradiant instability of massive vector fields around spinning black holes in the relativistic regime

## TL;DR

This paper investigates the superradiant instability of massive vector (Proca) fields around rapidly spinning black holes using time-domain simulations, revealing enhanced instability and stronger gravitational wave signals in the relativistic regime.

## Contribution

It provides the first detailed analysis of Proca field instabilities in the relativistic regime, showing increased instability range and gravitational wave strength compared to scalar fields.

## Key findings

- Relativistic effects extend the instability range for Proca fields.
- Maximum instability rates are higher in the relativistic regime.
- Gravitational waves sourced by Proca instabilities can be significantly stronger.

## Abstract

We study the superradiant instability of massive vector fields, i.e. Proca fields, around spinning black holes in the test field limit. This is motivated by the possibility that observations of astrophysical black holes can probe the existence of ultralight bosons subject to this mechanism. By making use of time-domain simulations, we characterize the growth rate, frequency, spatial distribution, and other properties of the unstable modes, including in the regime where the black hole is rapidly spinning and the Compton wavelength of the Proca field is comparable to the black hole radius. We find that relativistic effects in this regime increase the range of Proca masses that are unstable, as well as the maximum instability rate. We also study the gravitational waves that can be sourced by such an instability, finding that they can be significantly stronger than in the massive scalar field case.