New aspects of black hole scalarization in alternative theories of gravity

This thesis investigates the spontaneous scalarization of black holes in extended gravity models. We study two scenarios in which a scalar field develops non-trivial configurations (“hair”) around charged black holes. In the first scenario, a charged black hole is subject to both a tachyonic (instability-driven) coupling and a non-linear self-interaction, leading to \emph{mixed scalarization}. We show that the tachyonic coupling dominates the scalarization, while the non-linear coupling slightly extends the range of hairy solutions and influences their stability and entropy. In the second scenario, we propose a new model where the scalar field couples to both the Gauss--Bonnet curvature and the electromagnetic field. The combined couplings widen the parameter space for scalarized black holes, allowing scalar hair to form under conditions (such as negative curvature coupling or charge beyond the extremal limit) where it was previously forbidden. The scalarized solutions in both cases typically have higher entropy than their bald counterparts, and we discuss their stability under perturbations. Our results broaden the understanding of black hole scalarization and provide a foundation for further studies on the stability and observational consequences of hairy black holes.