Effects of mass and self-interaction on nonlinear scalarization of scalar-Gauss-Bonnet black holes

TL;DR

This paper investigates how scalar field mass and self-interaction influence the nonlinear scalarization of scalar-Gauss-Bonnet black holes, revealing that positive self-interaction suppresses scalarization while negative enhances it, with minimal effect on the jump phenomenon.

Contribution

It extends previous studies by analyzing the effects of scalar field potential, especially mass and self-interaction, on black hole scalarization in scalar-Gauss-Bonnet gravity.

Findings

Mass and positive self-interaction suppress scalarization.

Negative self-interaction enhances scalarization.

The jump between solutions is insensitive to the scalar potential.

Abstract

It was recently found that in certain flavours of scalar-Gauss-Bonnet gravity linearly stable bald black holes can co-exist with stable scalarized solutions. The transition between both can be ignited by a large nonlinear perturbation, thus the process was dubbed non-linear scalarization, and it happens with a jump that leads to interesting astrophysical implications. Generalizing these results to the case of nonzero scalar field potential is important because a massive self-interacting scalar field can have interesting theoretical and observational consequences, e.g. reconcile scalar-Gauss-Bonnet gravity with binary pulsar observation, stabilize black hole solutions, etc. That is why in the present paper, we address this open problem. We pay special attention to the influence of a scalar field mass and self-interaction on the existence of scalarized phases and the presence of a jump between stable bald and hairy back holes. Our results show that both the addition of a mass and positive self-interaction of the scalar field result in suppression or quenching of the overall scalarization phenomena. A negative scalar field self-interaction results in an increase of the scalarization. The presence and the size of the jump, though, are not so sensitive to the scalar field potential.