Sine-Gordon solitonic scalar stars and black holes

TL;DR

This paper presents exact solutions in Einstein-scalar gravity with sine-Gordon scalar fields, including a horizonless solitonic star and a black hole, analyzing their properties and stability.

Contribution

It introduces new analytic solutions featuring sine-Gordon scalar fields, including a regular solitonic star and a black hole, expanding the landscape of scalar-gravity configurations.

Findings

The solitonic scalar star is regular, horizonless, and interpolates between AdS and flat spacetime.

The black hole solution is unstable against linear perturbations.

Stability of the star-like solution remains uncertain due to numerical challenges.

Abstract

We study exact, analytic, static, spherically symmetric, four-dimensional solutions of minimally coupled Einstein-scalar gravity, sourced by a scalar field whose profile has the form of the sine-Gordon soliton. We present a horizonless, everywhere regular and positive-mass solution (a solitonic star) and a black hole. The scalar potential behaves as a constant near the origin and vanishes at infinity. In particular, the solitonic scalar star interpolates between an anti-de Sitter and an asympototically flat spacetime. The black-hole spacetime is unstable against linear perturbations, while due to numerical issues, we were not able to determine with confidence whether or not the star-like background solution is stable.