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Study of the Relativistic Dynamics of Extreme-Mass-Ratio Inspirals

Abstract : The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime---that is, where one mass is significantly smaller than the other---in the full context of our contemporary theoryof gravity, general relativity. We divide this work into two broad parts: the first provides an overview of thetheory of general relativity along with the basic mathematical methods underlying it, focusing on its canonicalformulation and perturbation techniques; the second presents our novel work in these areas, focusing on theproblems of entropy, motion and the self-force in general relativity. We begin here with a study of entropytheorems in classical Hamiltonian systems, and in particular, the issue of the second law of thermodynamicsin classical mechanics and general relativity. Then, we develop a general approach based on conservationlaws for calculating the correction to the motion of a sufficiently small object due to gravitational perturbationsin general relativity. When the perturbations are attributed to the small object itself, this effect is known as thegravitational self-force. It is what drives the orbital evolution of extreme-mass-ratio inspirals: compact binarysystems where one mass is much smaller than---thus effectively orbiting and eventually spiralling into---theother, expected to be among the main sources for the future space-based gravitational wave detector LISA.Finally, we present some work on the numerical computation of the scalar self-force using an approachcalled the Particle-without-Particle method, as well as the generalization of this method to general partialdifferential equations and applications to other areas of applied mathematics.Keywords : general relativity, gravitational two-body problem, gravitational self-force.
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Marius Oltean. Study of the Relativistic Dynamics of Extreme-Mass-Ratio Inspirals. General Relativity and Quantum Cosmology [gr-qc]. Université d'Orléans; Universitat autònoma de Barcelona, 2019. English. ⟨NNT : 2019ORLE2011⟩. ⟨tel-02865213⟩

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