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Einstein-Maxwell-scalar black holes with massive and self-interacting scalar hair

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.