New perspectives on scalar fields in strong gravity

Recent developments in the field of gravitational physics, including the emergence of gravitational wave astronomy, black hole images, and more accurate telescopes, have allowed us to probe the strong-field character of gravity in a novel and revolutionary manner. This accessibility related to strong gravity brings into the foreground discussions about potential modifications to General Relativity (GR) that are particularly relevant in high curvature regimes. The most straightforward way to generalize GR is to consider an additional degree of freedom, in the form of a scalar field. In this thesis, we study generalized scalar tensor theories that predict interesting strong-gravity phenomenology. First, we review scalar no-hair theorems and the conditions under which they can be evaded. Next, we study solutions of black holes with scalar hair and the way in which higher derivative terms alter their properties. We then move our discussion to the spontaneously scalarized solutions, which only deviate from GR in the strong-field regime. We propose a model consistent with compact object scalarization, that allows for a GR attractor at late times, without fine-tuning (EsRGB model). Then, we proceed to study properties of black holes and neutron stars in this theory, revealing the interesting phenomenology of the solutions. We also study the radial stability of black holes in EsRGB and perform a preliminary analysis of the hyperbolicity of the problem. Finally, we take a look at the shadows of black holes and wormholes in theories with scalar fields, in light of recent observations of black hole shadows.