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We study scalar fields in a black hole background and show that, when thescalar is suitably coupled to curvature, rapid rotation can induce a tachyonicinstability. This instability, which is the hallmark of spontaneousscalarization in the linearized regime, is expected to be quenched bynonlinearities and endow the black hole with scalar hair. Hence, our resultsdemonstrate the existence of a broad class of theories that share the samestationary black hole solutions with general relativity at low spins, but whichexhibit black hole hair at sufficiently high spins ($a/M\gtrsim 0.5$). Thisresult has clear implications for tests of general relativity and the nature ofblack holes with gravitational and electromagnetic observations.

Spin-induced black hole spontaneous scalarization