Gravitational collapse, compact objects and gravitational waves in General Relativity and modified gravity

Since the upgrade of the two LIGO Detectors it has been an exciting time for General Relativity (GR) research, as soon after they were upgraded to advanced status GW150914, the first gravitational wave signal from the inspiral and merger of two black holes was detected. The following consistent detections (9 further black hole binaries and one neutron star system) and the introduction of the European interferometer Virgo, as well as other planned detectors such as KAGRA and IndiGO mark the start of a new era of Gravitational Wave Physics and Astrophysics. This provides us with a window into the dynamics of strong gravity as well as the opportunity to test modified gravity and alternative theories in the strong regime, by confirming deviations from GR or constraining such theories. Why is General Relativity not enough though? It has passed all the tests so far with flying colors; in addition, the gravitational waves detected so far have demonstrated excellent agreement with GR’s predictions. Despite all these successful tests, there are still important questions related to Dark Energy and Dark Matter left unexplained. As a consequence, a clearer understanding of modified gravity theories is needed as well as a catalogue of gravitational waves resulting from these theories that could be used in the analysis of interferometer data and for stochastic background and continuous wave searches. In this Thesis we provide source modelling for GR and one of the most popular candidates for modified gravity, Scalar Tensor (ST) theories, as well as look for smoking-gun signatures. We analyse the formation of compact objects from core collapse simulations of stars in massive ST theories over the astrophysically plausible range of stellar progenitor masses and metallicities, as well as a large part of the parameter space of this class of modified theories of gravity. Next we test the robustness of our results by expanding the simulations to ST theories with self-interacting potentials. Finally, we study the recoil resulting from black holes mergers by varying the orbital eccentricity in an attempt to amplify the kicks