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Analytical methods for the study of the two-body problem, and alternative theories of gravitation

Abstract : The work completed during this thesis aimed at pushing forward our knowledge of gravitational phenomena, by following two directions: (i) deepening our comprehension of the relativistic two-body problem, (ii) building and testing alternative models. First, we used a post-Newtonian (weak-field and slow motion) approximation to seek analytic expressions for the phase of gravitational waves at high accuracy. Two of the main results of this thesis are thus the proper dimensional regularization of the mass quadrupole, and of the non-linear "tail'' and "memory'' effects, appearing in the radiative quadrupole.Using synergies with other approaches, we have also derived the logarithmic tail contributions in the conserved energy at high accuracies. Finally, and as a side result, we have also proposed the first realistic test of GR in an exoplanetary system. As for the second direction, we have investigated non-canonical domain walls by building a new class of non-topological kinks. We have shown that those were stable, and could mimic the canonical ones. A "minimal theory of bigravity'' was also constructed by requiring to avoid observationally unnecessary gravitational polarizations, and its cosmology was proven stable. Finally, we have investigated the strong-field regime of two of such minimal theories by deriving their (non-trivial) black hole solutions.
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Submitted on : Wednesday, December 8, 2021 - 4:23:07 PM
Last modification on : Sunday, June 26, 2022 - 3:23:47 AM


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  • HAL Id : tel-03471058, version 2


François Larrouturou. Analytical methods for the study of the two-body problem, and alternative theories of gravitation. General Relativity and Quantum Cosmology [gr-qc]. Sorbonne Université, 2021. English. ⟨NNT : 2021SORUS106⟩. ⟨tel-03471058v2⟩



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