Instability and backreaction of massive spin-2 fields around black holes

TL;DR

This paper investigates the instability of massive spin-2 fields around black holes using time-domain simulations, revealing how black hole spin influences instability growth and exploring nonlinear evolution effects in quadratic gravity.

Contribution

It provides the first detailed analysis of superradiant and Gregory-Laflamme instabilities for massive spin-2 fields on Kerr backgrounds, including nonlinear evolutions in quadratic gravity.

Findings

Black hole spin increases the growth rate and mass range of the $m=0$ instability.

Superradiant modes grow slower than $m=0$ modes, except at high spins.

Black holes can either evaporate or stabilize with a ghost spin-2 cloud depending on initial conditions.

Abstract

A massive spin-2 field can grow unstably around a black hole, giving rise to a potential probe of the existence of such fields. In this work, we use time-domain evolutions to study such instabilities. Considering the linear regime by solving the equations generically governing a massive tensor field on the background of a Kerr black hole, we find that black hole spin increases the growth rate and, most significantly, the mass range of the axisymmetric (azimuthal number $m=0$) instability, which takes the form of the Gregory-Laflamme black string instability for zero spin. We also consider the superradiant unstable modes with $1 \leq m \leq 3$, extending previous results to higher spin-2 masses, black hole spins, and azimuthal numbers. We find that the superradiant modes grow slower than the $m=0$ modes, except for a narrow range of high spins and masses, with $m=1$ and 2 requiring a dimensionless black hole spin of $a_{\rm BH}\gtrsim 0.95$ to be dominant. Thus, in most of the parameter space, the backreaction of the $m=0$ instability must be taken into account when using black holes to constrain massive spin-2 fields. As a simple model of this, we consider nonlinear evolutions in quadratic gravity, in particular Einstein-Weyl gravity. We find that, depending on the initial perturbation, the black hole may approach zero mass with the curvature blowing up in finite time, or can saturate at a larger mass with a surrounding cloud of the ghost spin-2 field.