Spin-Induced Nonlinear Scalarization of Kerr Black Holes in Einstein-scalar-Gauss-Bonnet Gravity

TL;DR

This paper explores a nonlinear spin-induced scalarization mechanism in Kerr black holes within Einstein-scalar-Gauss-Bonnet gravity, revealing a finite high-spin domain where scalar hair develops strongly.

Contribution

It demonstrates a genuinely nonlinear scalarization process without linear instability and constructs scalarized black hole solutions with a unique finite spin-mass domain.

Findings

Scalarization occurs above a spin threshold of 0.5.

Scalar hair strength increases toward high-spin extremal black holes.

Scalarized solutions form a finite wedge in the spin-mass plane.

Abstract

We investigate spin-induced scalarization of Kerr black holes in an Einstein-scalar-Gauss-Bonnet (EsGB) model that does not admit a linear tachyonic instability of the scalar-free solution. The scalarization mechanism is therefore genuinely nonlinear. We first analyze the decoupled scalar dynamics on fixed Kerr backgrounds and show that sufficiently rapid rotation modifies the Gauss-Bonnet invariant such that a negative near-horizon region develops near the poles. This region provides a geometric trapping mechanism for nonlinear scalar growth, which becomes effective above a threshold spin $\chi=0.5$. We then construct stationary scalarized black hole solutions with full backreaction and determine their domain of existence. We find that the solutions occupy a finite low-mass high-spin wedge in the spin-mass plane. This is in contrast to spin-induced spontaneous scalarization, where the scalarized solutions form a narrow band. In this wedge, toward the high-spin end, the scalar hair becomes stronger, and the solutions approach a near-extremal regime, while toward the low-spin boundary, the scalar field is strongly suppressed and approaches a weak-hair limit as $\chi \to 0.5$.