Eve Dones :
Team : ASTRE
Supervisor : Laura Bernard
The main sources of gravitational waves in the Universe are the compact binary systems composed of black holes, neutron stars, or more exotic objects. They orbit around each other while loosing energy in the form of gravitational waves, causing their orbit to shrink until they eventually merge. Detecting and analyzing these signals with current (LIGO-Virgo-Kagra) and future (Einstein Telescope, LISA, etc.) highly sensitive gravitational wave detectors requires a catalog of extremely accurate theoretical waveform models.
Although the two-body problem in general relativity does not have an exact solution in general, several perturbative approximation schemes have been developed to describe the different phases of a binary system’s coalescence. In particular, the inspiral phase, during which the two objects are far apart and orbit sufficiently slowly, is modeled using the post-Newtonian (PN) formalism. In that small velocities and weak gravitational field regime, the solutions of the problem can be expanded in power series in a small parameter $\epsilon=v/c$, where $v$ stands for the relative velocity of the objects, and c is the speed of light. The PN formalism enables a precise determination of the phase and the amplitude of the emitted waveform, which are key observables for gravitational wave data analysis.
Several challenges are currently beeing adressed in the theoretical waveform modeling. One major open question is the influence of neutron star matter on a binary system’s dynamics and radiation. The study of these effects is particularly promising to constrain the equations of states describing best these very complex systems. Another active area of research focuses on the gravitational wave modeling in alternative theories of gravity. So far, very few gravitational wave templates exist in theories beyond general relativity, yet they are essential for carrying out theory-dependent tests. Indeed, although no deviation from general relativity has yet been detected, there are strong motivations for modifying it, in particular to explain the accelerating expansion of the Universe. However, the very high precision of the expected data with the next generation gravitational wave detectors presents us with new challenges, including disentangling effects due to modifications of gravity from those arising from neutron star matter. It is therefore necessary to develop waveforms for the analysis that consider both effects at the same time.
This thesis is dedicated to the study of tidal effects in gravitational waveforms, both in alternative gravity theories and in general relativity, within the PN framework. The first part focuses on tidal effects in scalar-tensor theories, incorporating corrections up to the second order in the post-Newtonian development. In these theories, tides result from both companion-induced deformation and the presence of a scalar field. We studied the impact of these effects on the system’ dynamics and radiation, including tidal corrections to the phase and amplitude modes of the waveform. The second part of this thesis has been devoted to the study of the tidal effects in the context of general relativity up to the second and a half PN order. In particular, we derived tidal contributions to the waveform’s amplitude modes, which are crucial for comparison with numerical relativity predictions for the waveform emitted during the merger phase. These results provide valuable tools to probe the interior of neutron stars and to test the validity of alternative theories of gravitation.
