Black hole hair formation in shift-symmetric generalised scalar-tensor gravity

TL;DR

This paper investigates the dynamical formation of scalar hair around black holes in a shift-symmetric scalar-tensor gravity theory, demonstrating through numerical evolution that scalar fields relax to known hairy black hole configurations.

Contribution

It provides the first numerical study of scalar hair formation in shift-symmetric scalar-tensor gravity, confirming that collapse leads to static hairy black hole solutions.

Findings

Scalar fields relax to static hairy black hole configurations

Dynamical formation of scalar hair during collapse

Supports the endpoint of collapse being a hairy black hole

Abstract

A linear coupling between a scalar field and the Gauss-Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole or a collapsing dust star described by the Oppenheimer-Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.