This thesis investigates black-hole solutions in alternative theories of gravity, specifically those that emerge via the scalarization mechanism. 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 interaction, leading to mixed scalarization. We show that the tachyonic coupling dominates the scalarization, while the non-linear coupling slightly enlarges the domain of hairy solutions and affects their stability and entropy.

In the second scenario, we propose a new model of spontaneous scalarization in which the scalar field couples simultaneously to the Gauss–Bonnet curvature invariant and to a U(1) gauge field (interpretable as a dark photon or the electromagnetic field). This construction generalizes earlier single-coupling setups and permits both curvature-induced and matter-induced scalarization within one framework, overcoming the limitations of each mechanism alone. The combined couplings widen the parameter space for scalarized black holes, allowing scalar hair to form under relaxed conditions (such as negative curvature coupling or sub-extremal charge) where it was previously forbidden. We derive a new class of scalarized black-hole solutions that emerge at distinct mass thresholds, possess higher entropy than their Reissner–Nordström counterparts, and can even become overcharged, surpassing the usual extremal charge-to-mass limit. Our analysis also suggests that including the matter coupling may stabilize solutions that were previously prone to radial instabilities in pure Gauss–Bonnet models with quadratic coupling, making this extended model a promising candidate for further studies in strong-gravity regimes. These results broaden the understanding of black-hole scalarization and provide a basis for future investigations of observational signatures of black holes in modified theories of gravity.