Tidal deformations of compact objects and gravitational wave emission

Neutron stars are one of the most compact astronomical objects. The composition of matter in the inner part of their core is currently uncertain. Detections of gravitational waves emitted from the coalescence of binary neutron stars can be exploited to constrain the equation of state of nuclear matter. The information on the internal structure of the stars is encoded in their tidal deformabilities, which leave an imprint in the waveform of the gravitational signal emitted by the binary system. In my PhD thesis, I have extended the theory of tidal deformations of compact objects in general relativity, computing the leading order corrections to the gravitational waveform due to the coupling between the tidal deformabilities and the spins of the stars in spinning binary systems. Furthermore, I have shown the feasibility of reconstructing the parameters of a phenomenological representation of the neutron star equation of state using measurements of tidal deformability obtained through gravitational wave detections.