• black holes
• modified gravity
• radial perturbations
• scalar-Gauss-Bonnet gravity
• stability analysis

Einstein’s General Relativity (GR) revolutionized our understanding of gravity, but has mostly been tested in its weak-field regime. The advent of gravitational wave (GW) astronomy permits to study gravity in the strong-field regime. Observations from current and future GW detectors like LIGO, Virgo, LISA, and ET enable tests of GR beyond null-tests, requiring an understanding of potential deviations. This necessitates studying black hole (BH) behavior when GR is modified, as most detected GW signals come from binary BH coalescences. Plus, GR faces challenges in strong-field scenarios, motivating investigations into modifications of the theory.
This work explores scalar-Gauss-Bonnet gravity (sGB), an extension of GR involving quadratic curvature terms (the Gauss-Bonnet invariant) coupled to a scalar field within the Einstein-Hilbert action. These additions represent the simplest extension of GR in high-curvature regimes that yields different BH solutions. Indeed, no-hair theorems do not apply in sGB theories, allowing BHs to have a non-trivial scalar degree of freedom. Hairy and GR Bhs can be simultaneously solutions through the Spontaneous BH Scalarization. This phenomenon presents two issues addressed by this thesis: the unexplained minimum mass of sGB scalarized BHs and the necessity for physical solutions to be stable under radial perturbations.
This research introduces original aspects on alternative BH solutions to GR ones, testable by current and future GW detectors.