Properties of Scalar Hairy Black Holes and Scalarons with Asymmetric Potential (2210.01313v1)

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.