# On the stability of scalarized black hole solutions in scalar-Gauss-Bonnet gravity

## TL;DR

This paper investigates the stability of scalarized black hole solutions in scalar-Gauss-Bonnet gravity, revealing that the form of the scalar coupling determines whether solutions are stable or unstable.

## Contribution

It clarifies how higher-order scalar-Gauss-Bonnet couplings influence the nonlinear stability of scalarized black holes.

## Key findings

- Quadratic couplings lead to unstable scalarized black holes.
- Exponential couplings can produce stable scalarized black hole solutions.
- Higher-order couplings control the nonlinear quenching of tachyonic instabilities.

## Abstract

Scalar-tensor theories of gravity where a new scalar degree of freedom couples to the Gauss-Bonnet invariant can exhibit the phenomenon of spontaneous black hole scalarization. These theories admit both the classic black holes predicted by general relativity as well as novel hairy black hole solutions. The stability of the hairy black holes is strongly dependent on the precise form of the scalar-gravity coupling. A radial stability investigation revealed that all scalarized black hole solutions are unstable when the coupling between the scalar field and the Gauss-Bonnet invariant is quadratic in the scalar, whereas stable solutions exist for exponential couplings. Here we elucidate this behavior. We demonstrate that, while the quadratic term controls the onset of the tachyonic instability that gives rise to the black hole hair, the higher-order coupling terms control the nonlinearities that quench that instability, and hence also control the stability of the hairy black hole solutions.