Dynamics of scalar hair with self-interactions around a Schwarzchild black hole

TL;DR

This study investigates how scalar hair forms and evolves around a Schwarzschild black hole, considering self-interactions and their effects on scalarization, energy flux, and radiation in scalar Gauss-Bonnet gravity.

Contribution

It provides a perturbative analysis of scalar hair dynamics with self-interactions around a Schwarzschild black hole, including energy flux and scalarization effects.

Findings

Scalar hair formation depends on self-interactions.

Energy flux varies with different self-interaction strengths.

Results enhance understanding of scalarization in scalar Gauss-Bonnet gravity.

Abstract

In this paper, we study the dynamics of scalar hair around a Schwarzchild black hole. The scalar hair is sourced by the Gauss-Bonnet invariant with a linear coupling. We work perturbatively in the coupling constant and ignore the back-reaction of the scalar hair and the Gauss-Bonnet invariant. We evolve the scalar field in the background of a Schwarzchild black hole and study the dynamical formation of scalar hair with different self-interactions. We integrate the energy and compute the energy flux of the scalar hair in terms of the canonical energy-momentum tensor and give the corresponding dependence on the self-interactions. Our results allow us to estimate the radiation and the condensation of scalar field with different self-interactions, these would improve our understanding for the dynamical scalarization of black holes and the possible configuration of the scalar hair in scalar Gauss-Bonnet gravity.