Thesis title: Tidal deformations of rotating compact objects
The tidal perturbation of a compact body gives rise to its deformation, and hence induces a new multipolar structure on it. This
multipolar structure is fully characterised by a set of parameters, called the tidal Love numbers, which depend on the features of the body
itself, and therefore contain information on the matter that forms it. On the other hand, tidal Love numbers are also the parameters
that encode the contribution of tidal effects for the gravitational wave signal emitted during the late inspiral stage of a binary coalescence. Thus,
given an accurate model and enough detector precision, the observation of gravitational waves coming from such a system can give
us insights into the nature of the bodies that compose it. In the particular case of neutron stars, the tidal Love numbers
depend on the equation of state of its interior fluid, thus being a window into the behaviour of matter at supranuclear densities.
When considering rotating compact objects, the coupling between its angular momentum and an external tidal field gives rise to a new class of "rotational" tidal Love numbers. In our work we have computed these quantities for several equations of state. We also provide numerical evidence for a surprising "hidden" symmetry among the rotational tidal Love numbers with opposite parities, which are associated to perturbations
belonging to separate sectors. This symmetry, whose existence had been suggested on the basis of a Lagrangian description of the tidal
interaction in a binary system, holds independently of the equation of state of the star.
Furthermore, tidal-rotation effects, of which the rotational tidal Love numbers, have been found to enter the post-Newtonian graviational
waveform of a binary inspiral at 6.5 post-Newtonian order. We consider the impact that neglecting these effects has on the parameter
estimation by third-generation detectors, finding that they may lead to significant errors for neutron stars with spins as large as
$\sim$ 0.1. By performing a Fisher matrix analysis we also assess the measurability of rotational tidal Love numbers, showing that their
contribution to the waveform could be measured by third-generation detectors. Our results suggest that current models of tidal deformation
in late inspiral should be improved in order to avoid waveform systematics and extract reliable information from gravitational wave
signals observed by next generation detectors.