Compact objects and gravitational waves. Exploring fundamental physics with tidal effects

Abstract
In this thesis we study the role of relativistic tidal effects in binary systems of compact objects and their link to fundamental physics and gravitational waves. In particular, we develop theoretical frameworks to systematically and rigorously connect the microphysical information encoded in the compact object, with the dynamical spacetime of the binary, relevant for current and future gravitational-wave observations. We start with an overview of gravitational-wave theory and tidal effects before discussing our three lines of novel work. First, we generalise the relativistic treatment of tidal effects to gravity theories beyond general relativity which give rise to scalar hair in compact objects. We uncover a new set of tidal deformabilities and compute numerical values for neutron stars in scalar-tensor theories. We assess degeneracies between internal structure and gravity theories and extract the key parameters relevant for gravitational wave observations. Second, we calculate in detail the effects on the waveform and study the role and implications that these new parameters have for gravitational wave signals of coalescing binary systems. Furthermore, we develop a novel formalism to include the quasi-normal mode structure in a frequency-dependent dynamical tidal response function from gauge-invariant scattering amplitudes. In particular, this formalism overcomes previous difficulties with unambiguous identifications of information from strong-field regimes. As a case study, we apply our formalism to scalar perturbations of a Schwarzschild black hole and recover results from previous literature on the absorption cross section and tidal Love number. Additionally, we investigate the role played by analytic continuation to resolve degeneracies between post-Newtonian corrections, characterising relativistic effects in the binary, and multipolar expansions, encoding the finite size of the bodies.