Properties of Scalar Hairy Black Holes and Scalarons with Asymmetric Potential

TL;DR

This paper investigates the properties and stability of scalar hairy black holes and scalarons in Einstein gravity with an asymmetric scalar potential, revealing their unstable nature under radial perturbations.

Contribution

It introduces a detailed analysis of asymptotically flat hairy black holes and scalarons with an asymmetric potential, including their existence and stability characteristics.

Findings

Hairy black hole solutions emerge from Schwarzschild black holes.

Scalarons can be reached in the small horizon limit.

All studied solutions are unstable under radial perturbations.

Abstract

In this paper we study the properties of black holes and scalarons in Einstein gravity when it is minimally coupled to a scalar field $\phi$ with an asymmetric potential $V(\phi)$, constructed in [Phys. Rev. D \textbf{73} (2006), 084002] a few decades ago. $V(\phi)$ has been applied in the cosmology to describe the quantum tunneling process from the false vacuum to the true vacuum and contains a local maximum, a local minimum (false vacuum) and a global minimum (true vacuum). In particular we focus on the asymptotically flat solutions, which can be constructed by fixing appropriately the local minimum of $V$. A branch of hairy black holes solutions emerge from the Schwarzschild black hole, and we study the domain of existence of such configurations. They can reach to a particle-like solution in the small horizon limit, i.e. the scalarons. We study the stability of black holes and scalarons, showing that all of them are unstable under radial perturbations.