Novel exact ultra-compact and ultra-sparse hairy black holes emanating from regular and phantom scalar fields

TL;DR

This paper introduces new analytic black hole solutions with scalar hair in a simple gravity-scalar field model, revealing ultra-compact and ultra-sparse black holes with potential astrophysical implications.

Contribution

It presents the first analytic solutions for ultra-compact and ultra-sparse black holes arising from regular and phantom scalar fields, including their rotating and perturbation properties.

Findings

Regular scalar fields produce ultra-compact black holes.

Phantom scalar fields generate ultra-sparse black holes.

Stable solutions exist within certain parameter regions.

Abstract

In the framework of a simple gravitational theory that contains a scalar field minimally coupled to gravity, we investigate the emergence of analytic black-hole solutions with non-trivial scalar hair of secondary type. Although it is possible for one to obtain asymptotically (A)dS solutions using our setup, in the context of the present work, we are solely interested in asymptotically flat solutions. At first, we study the properties of static and spherically symmetric black-hole solutions emanating from both regular and phantom scalar fields. We find that the regular-scalar-field-induced solutions are solutions describing ultra-compact black holes, while the phantom scalar fields generate ultra-sparse black-hole solutions. The latter are black holes that can be potentially of very low density since, contrary to ultra-compact ones, their horizon radius is always greater than the horizon radius of the corresponding Schwarzschild black hole of the same mass. Then, we generalize the above static solutions to slowly rotating ones and compute their angular velocities explicitly. Finally, the study of the axial perturbations of the derived solutions takes place, in which we show that there is always a region in the parameter space of the free parameters of our theory that allows the existence of both ultra-compact and ultra-sparse black holes.