Effective stability against superradiance of Kerr black holes with synchronised hair

Understand

Kerr black holes with synchronised hair [arXiv:1403.2757, arXiv:1603.02687] are a counter example to the no hair conjecture, in General Relativity minimally coupled to simple matter fields (with mass $\mu$) obeying all energy conditions.

• Since these solutions have, like Kerr, an ergoregion it has been a lingering possibility that they are afflicted by the superradiant instability, the same process that leads to their dynamical formation from Kerr.
• A recent breakthrough [arXiv:1711.08464] confirmed this instability and computed the corresponding timescales for a sample of solutions.
• We discuss how these results and other observations support two conclusions: $1)$ starting from the Kerr limit, the increase of hair for fixed coupling $\mu M$ (where $M$ is the BH mass) increases the timescale of the instability; $2)$ there are hairy solutions for which this timescale, for astrophysical black hole masses, is larger than the age of the Universe.