Black holes, with their extreme gravitational fields, provide a crucial testing ground for theories of gravity beyond Einstein's General Relativity. In recent years, an active area of research has focused on scalar-tensor theories, where a scalar field couples to higher-curvature terms in the gravitational action. These theories predict black hole solutions that can differ substantially from the well-known Schwarzschild and Kerr solutions of General Relativity.

Characteristic properties of these alternative black holes include the emergence of intrinsic instabilities, different shadow morphologies, and unique gravitational wave spectra. These observable features not only distinguish these solutions from those predicted by General Relativity but also provide a means to set observational constraints on the coupling parameters of the underlying theories. The detection of gravitational waves and the observation of black hole shadows, for example, open new avenues for probing the validity of these gravitational extensions.