  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.
