Dynamical scalar hair formation around a Schwarzschild black hole

TL;DR

This paper investigates how scalar fields coupled to the Gauss-Bonnet invariant dynamically form scalar hair around Schwarzschild black holes, demonstrating evolution towards known static solutions.

Contribution

It provides the first detailed study of the dynamical formation process of scalar hair in this context, highlighting the evolution from initial conditions to static solutions.

Findings

Scalar hair forms dynamically around Schwarzschild black holes.

Evolution converges to static hairy solutions.

Shift-symmetric scalar fields evade no-hair theorems.

Abstract

Scalar fields coupled to the Gauss-Bonnet invariant evade the known no-hair theorems and have nontrivial configurations around black holes. We focus on a scalar field that couples linearly to the Gauss-Bonnet invariant and hence exhibits shift symmetry. We study its dynamical evolution and the formation of scalar hair in a Schwarzschild background. We show that the evolution eventually settles to the known static hairy solutions in the appropriate limit.