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Aspects of Geodesics and Gravitational Waves in Kerr Spacetime

par Liu, Yan
Président du jury Collinucci, Andrés
Promoteur Compère, Geoffrey
Publication Non publié, 2022-05-31

Thèse de doctorat

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Résumé :

In recent years, the direct detection of gravitational waves and the appearance of the black hole picture directly proved the correctness of the general relativity in the strong field regime. The future mission of the ground-based and space-based observatories on the detection of potential signals from the intermediate mass-ratio coalescences and extreme mass ratio inspirals requires further development of the gravitational waveform models. Accurate modeling of their waveforms within general relativity can be achieved within black hole perturbation theory including self-force and finite size effects. The finite size effects, whose first effects are the spin effects, deviate the extended object away from its geodesic motion. The self force effects can also be seen as the perturbation of the timelike geodesics. Therefore, to develop these models, a deeper understanding about the geodesic motion is required as well.This thesis starts with the investigation of non-equatorial geodesic motion in Kerr spacetime. We classify radial timelike geodesic motion of the exterior non-extremal Kerr spacetime, the ergoregion, and the near-horizon extreme Kerr, by performing a taxonomy of inequivalent root structures of the first order radial geodesic equation, using a novel compact notation and by implementing the constraints from polar, time, and azimuthal motion. We derive the explicit phase space of all such root systems and classify whether each corresponding radial geodesic motion is allowed or disallowed from the existence of polar, time, and azimuthal motion. We explicitly parameterize the separatrix describing root systems with double roots as well.Furthermore, we investigate the spin and self force effects in near-horizon extreme Kerr. For simplicity, we discuss them separately. We present analytic results to the Teukolsky perturbation of equatorial orbits in the near horizon region of an extremely high spin black hole including spin coupling and finite size effects at leading order in the high spin limit while neglecting the self force. We detail the critical behavior occurring close to the smallest specific angular momentum, and we discuss features of spin and quadrupole couplings.Finally, we semi-analytically investigate the scalar self-force experienced in the final stages of mass ratio inspirals of nonspinning scalar particles into supermassive nearly extremal Kerr black holes. We exploit the near horizon conformal symmetry to find the self force for general corotating equatorial geodesics. We verify that the energy and angular momentum losses of the scalar particle match with the asymptotic fluxes of scalar radiation. In particular, we relate the previously described persistent oscillations in the asymptotic energy and angular momentum fluxes with the local self force.