Spin-induced black hole spontaneous scalarization

TL;DR

This paper demonstrates that rapid rotation in black holes can trigger a tachyonic instability in scalar fields, leading to scalar hair formation at high spins, which has implications for testing general relativity.

Contribution

It shows that spin-induced tachyonic instability can cause spontaneous scalarization in black holes, revealing new black hole solutions with scalar hair at high spins.

Findings

High-spin black holes can develop scalar hair due to tachyonic instability.

Scalarization occurs for spin parameters $a/M \,\gtrsim\, 0.5$.

Implications for observational tests of gravity and black hole properties.

Abstract

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.