Papers › Instability and backreaction of massive spin-2 fields around black holes
Instability and backreaction of massive spin-2 fields around black holes
William E. East, Nils Siemonsen
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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 ≤m ≤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_(BH)≳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.
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