  Recently, spontaneous scalarization of charged black holes has attracted a
great deal of attention and motivated several studies of
Einstein-Maxwell-scalar models. These studies have, however, only considered a
massless and non-self-interacting scalar field. In this work a more realistic
treatment of the problem is considered by studying the effects of scalar field
mass and self-interacting terms on spontaneous scalarization in
Einstein-Maxwell-scalar models, and on the string theory motivated dilatonic
black hole. We assess the domains of existence of the black hole solutions,
thermodynamic preference and radial profiles. Then we discuss on the stability
of the scalarized solutions, focusing on spherical perturbations, finding all
studied solutions to be stable.
