Our results go substantially beyond the state of the art. For instance:
• We have studied tidal effects to next-to-next-to leading PN order in scalar-tensor theories of gravity, studying the conservative dynamics and computing the conserved quantities.
• We have computed the tidal contributions to the full gravitational waveform in general relativity, to 2.5PN order.
• We have studied the dynamics of EMRIs in presence of scalar fields (either GR modifications or fundamental fields), extending previous results to non-equatorial orbits and to time-dependent scalar fields.
• We have studied QNMs for a wide range of BH mimickers, from regular black holes to horizonless objects, finding that their detection by next generation interferometers might be sensible to macroscopic values of the regularization parameter.
• We have clarified the phenomenon of spectral instability.
• We have studied quadratic QNMs, computing their amplitudes for Schwarzschild BHs, finding the ratio between their amplitudes and those of linear QNMs, and assessing their detectabiltiy by present and future GW detectors.
• We have computed, using different approaches (one of which developed by ourselves) the QNMs of GR with higher-derivative corrections, i.e. including in the action (in an EFT framework) quadratic and cubic terms in the curvature tensor.
• We have studied the excitation factors of QNMs for a spinning BH in GR, reconstructing the ringdown waveform in terms of the QNMs.
• We have studied the avoided crossing of modes in Kerr and Kerr-de Sitter BHs.
• We have studied the ringdown of dynamical spacetimes, focussing on the dynamical consequences of a change of mass due to accretion, and on dynamical lensing.
• We have addressed the problem of well-posedness of modified gravity theories with higher derivatives, applying an approach we had developed in the first part of the project, to a class of scalar-tensor theories, the K-Essence theories.
• Using NR simulation we studied the tail signal at the end of the ringdown, finding that it is stronger than previously expected, and within reach of GW detector measurements.
• We developed a novel method to construct initial data NR simulations, based on hyperboloidal slices and leads to simulations with increased numerical stability.
• We studied the nonlinear merger of two boson stars and characterized the corresponding gravitational-wave signal.
• We performed NR simulations to study the nonlinear ringdown of hairy black holes displaying features typically associated with horizonless objects, such as echoes.
• We have investigated the fuzzy DM model, studying the mixing between ultra-light bosons (e.g.axions or dark photons) and the photon.
• We have studied the superradiant instability of magnetically-charged, rotating BHs finding that a magnetic charge significantly reduces the instability timescale
• We studied the possibility of using the motion of S2 to constrain vector clouds around SgrA*, finding novel bounds on the vector mass from GRAVITY observations.
• We studied how PTA observations (NANOGrav and EPTA) can be intepreted as due to GWs induced by scalar fields or to primordial BHs, and how they can constrain modified gravity theories and ultra-light dark matter models.
• We studied how high-frequency GW detectors (based on cavities and circuits) may be used to detect ultra-light dark matter.
• We developed a data-analysis framework to forecast the sensitivity of future PTA configurations and to assess the parameter estimation of the stochastic GR background.
• We developed models of the binary BH population to find the expected statistical distribution of LISA sources.
• We studied the statistical properties of the GW signal from primordial BHs.
• We developed data-analysis models to study the ringdown. One of these models addresses the computation of the Bayes factor for the presence of the first overtone in the ringdown signal.
• We made an exhaustive analysis of possible causes of false GR violations in GW observations.
• We studied how, in the analysis of the GW signal from LISA binaries, the effect of stochastic gas torques affects the estimation of parameters.
