Spin-Induced Black Hole Spontaneous Scalarization

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.

Figure 1

Instability timescale $\tau$ (color code) for the reconstructed field as a function of spin and GB coupling. The instability threshold for the total reconstructed field is shown by the solid green line, while the threshold when the $m=0$ modes are excluded is shown by a blue dotted line. The red-dashed line corresponds the instability threshold for the $m=0$ odd modes, while the dot-dashed cyan line marks the instability threshold for the spherical mode $l=m=0$ (see text for details). Note that all shown values of $\eta$ are unconstrained by different observables (cf. discussion in the conclusions).

Figure 2

Energy flux ${\mathcal{F}}_E$ through the BH horizon vs time, for $a=0.99M$. The blue, orange, and magenta lines correspond, respectively, to $\eta =-10M^2$, to a tachyonic mass $\mu M=i$, and to a constant, real mass $\mu M=0.42$. The inset enlarges the constant, real mass flux (of which we show a moving average to decrease the oscillations caused by the dynamics). That flux is negative, signaling energy extraction from the BH, as expected for superradiant instabilities.