Tidal deformations of compact objects and gravitational wave emission

Observations of gravitational wave (GW) signals produced by coalescing binary neutron stars (NS), like the GW event GW170817, can be exploited to constrain the equation of state (EoS) of matter in the stars' inner core. The information on the internal structure and composition of the stars is encoded in their tidal Love numbers, which leave an imprint in the waveform of the GW signal emitted from the binary during the late inspiral phase. We extended the theory of tidal deformations of compact objects by computing the spin-tidal corrections that affect the dynamics and the GW emission of a binary system at the leading post-Newtonian (PN) order and to linear order in the spin. These corrections are divided into two classes: terms due to the coupling between the standard tidal Love numbers and the spins of the objects, and terms depending on the rotational tidal Love numbers. Both enter the GW phase at 6.5PN order. We analysed the impact of the spin-tidal couplings by estimating the parameter bias induced on GW170817-like events, assuming second- and third-generation ground based interferometers. If relatively high spinning ($\chi \gtrsim 0.1$) NS binaries exist in nature, these effects might be observed by the next generation of detectors. Lastly, we proved the feasibility of solving the so-called inverse stellar problem using GW detections, i.e., reconstructing the EoS from the measurement of NS masses and tidal Love numbers. Our results show that few observations of coalescing binary NS by a network of advanced detectors would allow us to put interesting constraints on the phenomenological parameters of a piecewise polytropic representation of the EoS, and to perform a model selection among the realistic EoS proposed in the literature.