Scalar hairy black holes and solitons in asymptotically flat spacetimes

TL;DR

This paper numerically investigates scalar-tensor gravity theories, revealing static black holes with scalar hair and regular scalar solitons in asymptotically flat spacetimes, challenging the no-hair conjecture.

Contribution

It demonstrates the existence of scalar-hairy black holes and solitons in asymptotically flat spacetimes within scalar-tensor theories, including cases with minimal coupling.

Findings

Scalar-hairy black hole solutions exist in these theories.

Regular scalar solitons are found as black hole horizons shrink.

Configurations with non-positive scalar potentials can be asymptotically flat.

Abstract

A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\phi)$ of the theory is not positive semidefinite and such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations for the minimal coupling case, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture. For the nonminimal coupling case, the stability will be analyzed in a forthcoming paper.