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Kerr black holes with synchronised hair [arXiv:1403.2757, arXiv:1603.02687]are a counter example to the no hair conjecture, in General Relativityminimally coupled to simple matter fields (with mass $\mu$) obeying all energyconditions. Since these solutions have, like Kerr, an ergoregion it has been alingering possibility that they are afflicted by the superradiant instability,the same process that leads to their dynamical formation from Kerr. A recentbreakthrough [arXiv:1711.08464] confirmed this instability and computed thecorresponding timescales for a sample of solutions. We discuss how theseresults and other observations support two conclusions: $1)$ starting from theKerr limit, the increase of hair for fixed coupling $\mu M$ (where $M$ is theBH mass) increases the timescale of the instability; $2)$ there are hairysolutions for which this timescale, for astrophysical black hole masses, islarger than the age of the Universe. The latter conclusion introduces thelimited, but physically relevant concept of effective stability. The formerconclusion, allows us to identify an astrophysically viable domain of sucheffectively stable hairy black holes, occurring, conservatively, for $M\mu\lesssim 0.25$. These are hairy BHs that form dynamically, from thesuperradiant instability of Kerr, within an astrophysical timescale, but whoseown superradiant instability occurs only in a cosmological timescale.

Effective stability against superradiance of Kerr black holes with synchronised hair