I investigate the self-force acting on static scalar and electric charges in Schwarzschild-de Sitter and Schwarzschild-Anti-de Sitter spacetimes. The self-force occurs when a charged particle's field interacts with the curvature of spacetime so that the particle interacts with its own field. Because the field of a point particle is singular at the location of the particle, it is necessary to decompose the field into a regular part responsible for the self-force and a singular part that does not contribute to the self-force. To do this, I use the mode-sum regularization scheme introduced by Barack and Ori, in which the field is decomposed into a sum over modes, and the singular part is removed from each mode using so-called regularization parameters. I find that the electrostatic self-force in Schwarzschild-de Sitter and Schwarzschild-Anti-de Sitter behaves similarly to Schwarzschild self-force near the black hole, but can deviate strongly at larger distances. This is especially true in Schwarzschild-Anti-de Sitter, where the self-force is seen to increase linearly with distance. I provide an explanation for this behaviour using conformal transformations. A particular feature evident in Schwarzschild-Anti-de Sitter is that the self-force can become negative (attractive) at small distances when the Schwarzschild radius and the cosmological length scale are of a similar order. I find that the scalar self-force in Schwarzschild-de Sitter can not actually be computed, and in Schwarzschild-Anti-de Sitter the asymptotic behaviour is similar to its electrostatic counterpart.

Cette thèse s'inscrit dans le cadre de la modélisation des ondes gravitationnelles et du mouvement relativiste associés aux systèmes binaires à grand rapport de masses (Extreme Mass Ratio Inspiral - EMRI). Ces systèmes sont formés d'un trou noir super massif autour duquel gravite un objet compact de masse stellaire. Dans le formalisme de la théorie perturbative des trous noirs, on développe une méthode numérique qui calcule les formes d'ondes produites par une particule ponctuelle en orbite autour d'un trou noir de Schwarzschild. Il s'agit de résoudre l'équation d’onde de Regge-Wheeler-Zerilli dans le domaine temporel dont la solution, invariante de jauge, peut être reliée aux modes de polarisation, à l'énergie et au moment cinétique emporté par les ondes gravitationnelles. En réaction à l'énergie et au moment perdu, la trajectoire de la particule est affectée au cours du temps. Dans le cadre du formalisme de MiSATaQuWa, on calcule la force propre agissant sur une particule, initialement au repos, est en chute libre sur un trou noir de Schwarzschild. Nous montrons comment cette quantité est définie dans la jauge de Regge-Wheeler par le biais de la régularisation mode-sum. L'effet de la force propre sur le mouvement de la particule est ensuite pris en compte de façon itérative et auto-consistante grâce à un algorithme utilisant une méthode d'orbites osculatrices que nous avons développé. Nous quantifions cet effet en calculant soit la déviation orbitale par rapport au mouvement géodésique, soit les formes d'ondes perturbées et l'énergie rayonnée associée. / This thesis focuses on modelling the gravitational waves and the relativistic motion associated to Extreme Mass Ratio Inspiral (EMRI) systems. These systems consist of a stellar mass compact object gravitationally captured by a super-massive black hole. In black hole perturbation theory, we further develop a numerical method which computes waveforms generated by a point mass particle orbiting a Schwarzschild black hole. The Regge-Wheeler-Zerilli wave equation is solved in time domain. The gauge invariant solution is related to the polarisation modes, the energy and the angular momentum carried by the gravitational waves. In reaction to the energy and the moment lost, the trajectory is modified all along. In the MiSaTaQuWa formalism, we compute the self-force acting upon a point particle which is initially at rest, and then falling into a Schwarzschild black hole. We show how this quantity is defined in the Regge-Wheeler gauge by using the mode-sum regularisation technique. We take into account the self-force effect on the motion of the particle by using an iterative and osculating orbit method conceived herein. We quantify the orbital deviation with respect to the geodesic motion, but also the perturbed wave forms and the associated radiated energy.

Meine kumulative Dissertation

Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T13:45:16Z No. of bitstreams: 1 arquivototal.pdf: 1340608 bytes, checksum: 8cceaa9c73ae05a5a903b4b78e3fa6ba (MD5) / Made available in DSpace on 2017-09-18T13:45:16Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1340608 bytes, checksum: 8cceaa9c73ae05a5a903b4b78e3fa6ba (MD5) Previous issue date: 2010-04-15 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / It is presented a review on three subjects: the origin and nature of topological defects, the non-relativistic and relativistic quantum mechanics, and the gravitational and eletrostatic selfforces that emerge from a conical spacetime surrounding a cosmic string. After setting up this theoretical framework, it is studied the behavior of a charged particle in the presence of a cosmic string, parallel to an uniform, constant magnetic field, which may be used as a model to a primordial large-scale magnetic field that permeates the universe. The geometry of a negative disclination is taken into account, this being a typically condensed matter physics topological defect equivalent to a cosmic string, where a wedge of material is inserted into the lattice. We computed exactly, the topological and electrostatic influences on the particles energy spectrum, and the phase shift for the charged scalar particle scattered states. Switching to a flat-spacetime context, spherically symmetric systems were studied, solving exactly, Klein-Gordon and Dirac equations which describe a scalar particle subject to a Coulomb vector potential and scalar central potentials. / Apresentamos uma revisão sobre a origem e a natureza dos defeitos topológicos, que surgem a partir de transições de fase que podem ter ocorrido no início do processo de formação do universo; sobre a mecânica quântica não-relativística e relativística; e sobre as auto-forças gravitacional e eletrostática que emergem da topologia cônica do espaço-tempo gerado pela corda cósmica. Utilizando estas ferramentas, estudamos o movimento de uma partícula carregada na presença de uma corda cósmica, paralela a um campo magnético uniforme, de magnitude constante, que poderia servir de modelo para um campo magnético primordial. Também consideramos a geometria anti-cônica de uma desclinação negativa, defeito topológico análogo à corda cósmica estudado em matéria condensada. Calculamos, exatamente, a influência da topologia e do campo magnético no espectro de energia da partícula e encontramos o ângulo de mudança de fase para seus estados espalhados. No espaço-tempo plano, estudamos sistemas com simetria esférica e investigamos a dinâmica de uma partícula escalar, resolvendo, exatamente, as equações de Klein-Gordon e Dirac, considerando potenciais centrais.