We study scalar fields in a black hole background and show that, when the scalar is suitably coupled to curvature, rapid rotation can induce a tachyonic instability. This instability, which is the hallmark of spontaneous scalarization in the linearized regime, is expected to be quenched by nonlinearities and endow the black hole with scalar hair. Hence, our results demonstrate the existence of a broad class of theories that share the same stationary black hole solutions with general relativity at low spins, but which exhibit black hole hair at sufficiently high spins ($a/M\gtrsim 0.5$). This result has clear implications for tests of general relativity and the nature of black holes with gravitational and electromagnetic observations.

中文翻译：

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自旋诱导的黑洞自发标量

我们研究了黑洞背景下的标量场，结果表明，当标量适当地与曲率耦合时，快速旋转会引起速动不稳定。这种不稳定性是线性化过程中自发标量化的标志，预计将通过非线性来消除，并为黑洞赋予标量头发。因此，我们的结果证明了存在一类广泛的理论，它们在低自旋下具有相同的固定黑洞解，并且具有广义相对论，但是在足够高的自旋下表现出黑洞毛发（$\mathrm{一种}/\mathrm{中号}\gtrsim 0.5$）。该结果对于用重力和电磁观测测试广义相对论和黑洞的性质具有明显的意义。