Born-Infeld stars and charged black holes surrounded by scalar clouds

We discuss the formation of scalar clouds on charged, spherically symmetric and static stars and black holes. We first discuss Reissner-Nordstr & ouml;m black holes with electric and magnetic charge and present new results demonstrating the existence of a second branch of solutions. Moreover, we find that the presence of the magnetic charge allows for a smaller mass and Noether charge when the clouds are close to their minimal possible mean radius. When replacing standard electrodynamics with Born-Infeld (BI) electrodynamics, the background model possesses globally regular, starlike solutions as well as black hole solutions. We show that the former can be scalarized as well, and that the scalar clouds become more compact when decreasing the electric charge of the BI star. Finally, we discuss a magnetic dipole field in the background of the scalarized BI star and show that the strong gravitational field of this star leads to a significant change.