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Abstract

It was recently shown that a scalar field suitably coupled to the
Gauss-Bonnet invariant $\mathcal{G}$ can undergo a spin-induced linear
tachyonic instability near a Kerr black hole. This instability appears only
once the dimensionless spin $j$ is sufficiently large, that is, $j \gtrsim
0.5$. A tachyonic instability is the hallmark of spontaneous scalarization.
Focusing, for illustrative purposes, on a class of theories that do exhibit
this instability, we show that stationary, rotating black hole solutions do
indeed have scalar hair once the spin-induced instability threshold is
exceeded, while black holes that lie below the threshold are described by the
Kerr solution. Our results provide strong support for spin-induced black hole
scalarization.