<p>Gravitational waves and electromagnetic waves are important as carriers of energy and information. This thesis is devoted to the study of the propagation and interaction of these waves in plasmas, with emphasis on nonlinear effects and applications within astrophysics.</p><p>The physical systems are described by the Einstein-Maxwell-fluid equations or Einstein-Maxwell-Vlasov equations, when a kinetic treatment is required. The small amplitude and high-frequency approximation is employed for the gravitational waves, such that perturbative techniques can be applied and space-time can be considered locally flat, with a gravitational radiation field superimposed on it. The gravitational waves give rise to coupling terms that have the structure of effective currents in the Maxwell equations and an effective gravitational force in the equation of motion for the plasma. The Einstein field equations describe the evolution of the gravitational waves, with the perturbed energy-momentum density of the plasma and the electromagnetic field as a source.</p><p>The processes that are investigated are gravitational waves exciting electromagnetic waves in plasmas, altering the optical properties of plasmas and accelerating charged particles. The thesis also deals with the propagation propertities of gravitational and electromagnetic waves, e.g. effects due to resonant wave-particle interactions, plasma inhomogeneties and nonlinear self-interactions. It is also shown that plasmas that are not in thermodynamical equilibrium may release their free energy by emitting gravitational waves.</p>

One of the most exciting predictions of Einstein's theory of gravitation that have not yet been proven experimentally by a direct detection are gravitational waves. These are tiny distortions of the spacetime itself, and a world-wide effort to directly measure them for the first time with a network of large-scale laser interferometers is currently ongoing and expected to provide positive results within this decade. One potential source of measurable gravitational waves is the inspiral and merger of two compact objects, such as binary black holes. Successfully finding their signature in the noise-dominated data of the detectors crucially relies on accurate predictions of what we are looking for. In this thesis, we present a detailed study of how the most complete waveform templates can be constructed by combining the results from (A) analytical expansions within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches for nonspinning systems by extending the accessible parameter space and introducing an alternative scheme based in the Fourier domain. Our methods can now be readily applied to multiple spherical-harmonic modes and precessing systems. In addition to that, we analyze in detail the accuracy of hybrid waveforms with the goal to quantify how numerous sources of error in the approximation techniques affect the application of such templates in real gravitational-wave searches. This is of major importance for the future construction of improved models, but also for the correct interpretation of gravitational-wave observations that are made utilizing any complete waveform family. In particular, we comprehensively discuss how long the numerical-relativity contribution to the signal has to be in order to make the resulting hybrids accurate enough, and for currently feasible simulation lengths we assess the physics one can potentially do with template-based searches. / Eine der aufregendsten Vorhersagen aus Einsteins Gravitationstheorie, die bisher noch nicht direkt durch ein Experiment nachgewiesen werden konnten, sind Gravitationswellen. Dies sind winzige Verzerrungen der Raumzeit selbst, und es wird erwartet, dass das aktuelle Netzwerk von groß angelegten Laserinterferometern im kommenden Jahrzehnt die erste direkte Gravitationswellenmessung realisieren kann. Eine potentielle Quelle von messbaren Gravitationswellen ist das Einspiralen und Verschmelzen zweier kompakter Objekte, wie z.B. ein Binärsystem von Schwarzen Löchern. Die erfolgreiche Identifizierung ihrer charakteristischen Signatur im Rausch-dominierten Datenstrom der Detektoren hängt allerdings entscheidend von genauen Vorhersagen ab, was wir eigentlich suchen. In dieser Arbeit wird detailliert untersucht, wie die komplettesten Wellenformenmodelle konstruiert werden können, indem die Ergebnisse von (A) analytischen Entwicklungen im post-Newtonschen Verfahren und (B) numerische Simulationen der voll-relativistischen Bewegungen verknüpft werden. Es werden verschiedene Verfahren zur Erstellung solcher "hybriden Wellenformen", bei denen der post-Newtonsche Teil mit numerischen Daten vervollständigt wird, analysiert. Existierende Strategien für nicht-rotierende Systeme werden vertieft und der beschriebene Parameterraum erweitert. Des Weiteren wird eine Alternative im Fourierraum eingeführt. Die entwickelten Methoden können nun auf multiple sphärisch-harmonische Moden und präzedierende Systeme angewandt werden. Zusätzlich wird die Genauigkeit der hybriden Wellenformen mit dem Ziel analysiert, den Einfluss verschiedener Fehlerquellen in den Näherungstechniken zu quantifizieren und die resultierenden Einschränkungen bei realen Anwendungen abzuschätzen. Dies ist von größter Bedeutung für die zukünftige Entwicklung von verbesserten Modellen, aber auch für die korrekte Interpretation von Gravitationswellenbeobachtungen, die auf Grundlage solcher Familien von Wellenformen gemacht worden sind. Insbesondere wird diskutiert, wie lang der numerische Anteil des Signals sein muss, um die Hybride genau genug konstruieren zu können. Für die aktuell umsetzbaren Simulationslängen wird die Physik eingeschätzt, die mit Hilfe von Modell-basierten Suchen potentiell untersucht werden kann.

Gravitational waves and electromagnetic waves are important as carriers of energy and information. This thesis is devoted to the study of the propagation and interaction of these waves in plasmas, with emphasis on nonlinear effects and applications within astrophysics. The physical systems are described by the Einstein-Maxwell-fluid equations or Einstein-Maxwell-Vlasov equations, when a kinetic treatment is required. The small amplitude and high-frequency approximation is employed for the gravitational waves, such that perturbative techniques can be applied and space-time can be considered locally flat, with a gravitational radiation field superimposed on it. The gravitational waves give rise to coupling terms that have the structure of effective currents in the Maxwell equations and an effective gravitational force in the equation of motion for the plasma. The Einstein field equations describe the evolution of the gravitational waves, with the perturbed energy-momentum density of the plasma and the electromagnetic field as a source. The processes that are investigated are gravitational waves exciting electromagnetic waves in plasmas, altering the optical properties of plasmas and accelerating charged particles. The thesis also deals with the propagation propertities of gravitational and electromagnetic waves, e.g. effects due to resonant wave-particle interactions, plasma inhomogeneties and nonlinear self-interactions. It is also shown that plasmas that are not in thermodynamical equilibrium may release their free energy by emitting gravitational waves.

Gravitational perturbations can be in the form of scalars, vectors or tensors. This thesis focuses on the evolution of scalar perturbations in cosmology, and interactions between tensor perturbations, in the form of gravitational waves, and plasma waves. The gravitational waves studied in this thesis are assumed to have small amplitudes and wavelengths much shorter than the background length scale, allowing for the assumption of a flat background metric. Interactions between gravitational waves and plasmas are described by the Einstein-Maxwell-Vlasov, or the Einstein-Maxwell-fluid equations, depending on the level of detail required. Using such models, linear wave excitation of various waves by gravitational waves in astrophysical plasmas are studied, with a focus on resonance effects. Furthermore, the influence of strong magnetic field quantum electrodynamics, leading to detuning of the gravitational wave-electromagnetic wave resonances, is considered. Various nonlinear phenomena, including parametric excitation and wave steepening are also studied in different astrophysical settings. In cosmology the evolution of gravitational perturbations are of interest in processes such as structure formation and generation of large scale magnetic fields. Here, the growth of density perturbations in Kantowski-Sachs cosmologies with positive cosmological constant is studied.

In this thesis, Newman-Penrose techniques are used to obtain some new exact solutions to Einstein's field equations of general relativity and to assist in the physical interpretation of some exact radiative space-times. Attention is restricted to algebraically special space-times with a twist-free, repeated principal null congruence. In particular, the Robinson-Trautman type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant A and the Gaussian curvature parameter E. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced along time-like, space-like or null lines, depending on E. Explicit sandwich waves of this class are studied in Minkowski, de Sitter or anti-de Sitter backgrounds and a particular family of such solutions, which can be used to represent snapping or decaying cosmic strings, is considered in detail. The singularity and global structure of the solutions is also presented. In the remaining part of the thesis, the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves), that are of algebraic type III and for which the cosmological constant (Ac) is non-zero, is presented. The possible presence of an aligned pure radiation field is also assumed. These space-times generalise the known vacuum solutions of type N with arbitrary Ac and type III with Ac = O. It is shown that there are two, one and three distinct classes of solutions when Ac is respectively zero, positive and negative and, in these cases, the wave surfaces are plane, spherical or hyperboloidal in Minkowski, de Sitter or anti-de Sitter backgrounds respectively. The singularities which occur in these space-times are interpreted in terms of envelopes of these wave surfaces. Again, by considering functions of the retarded time which "cross-over" between canonical types, sandwich waves are also studied. The limiting cases of these, giving rise to shock or impulsive waves, are also considered.

This thesis presents the research done towards the development of the final mirror suspension stage for the high power test facility at AIGO, Western Australia. One of the goals of the facility is to test advanced suspension methods that may be useful in future gravitational wave detectors. An in depth study of current mirror suspension techniques is presented and areas of possible improvement are highlighted. The extension of an existing suspension modelling toolkit written in Mathematica is also presented, where added functions allow one to include the violin modes of a suspension into their analysis. Through this tool, new suspension geometries boasting a lower number of violin modes with lower Q factors where developed. The orthogonal ribbon suspension and the thin tube suspension boast a lower number of lower Q violin modes compared to typical ribbon suspensions. For the latter, a reduction in the number of violin modes below 5kHz down to 5 and peak thermal noise amplitude by approximately 30dB is predicted. Presented also is the affect that such suspension geometries have on pendulum mode dilution factor and overall suspension thermal noise. It is seen that the violin mode improvement comes at a cost of a small increase in thermal noise above approximately 50Hz. A theoretical analysis of the AIGO cavity locking control scheme is also given. Issues of sensor noise and dynamic range are considered to produce a possible hierarchical locking method that would be compatible with advanced detectors. The resulting actuator force range requirements for AIGO at each actuation location on the vibration isolation system are given. Requirements of local controls before achieving cavity lock are also discussed. Finally, the suspension of a dummy sapphire mirror using removable modular niobium ribbons is presented. The design and performance of an electrostatic actuator and sensor for suspended mirror control is given. Initial experimental results of positioning and control of the final stage suspension through a digital interface is also included.

Advanced Laser Interferometric Gravitational Wave Detectors, based on current infrastructure (in particular, the Advanced LIGO detectors), are being planned to significantly increase the sensitivity to gravitational wave strain in the near future. To upgrade the existing detectors requests implementing very high optical power, as well as very high circulating power in the arm cavities; these measures will increase the sensitivity at the shot noise floor by one order of magnitude. However, such extremely high power circulation in the cavities will cause optical distortions in the test masses. Thermal distortions arise from the optical power absorption by defects or inhomogeneities in test masses, resulting in wavefront deformations, which have important consequences for the power buildup of the Radio-Frequency (RF) sidebands in the recycling cavities, thus degrading the performance of the detectors. The degree of this sensitivity degradation in the shot noise floor, due to optical distortions induced by defects or inhomogeneities (i.e. imperfections) in test masses in Advanced Laser Interferometric Gravitational-wave Detectors, is dependent on the test mass optical quality; while the sensitivity degradation in the thermal noise floor is dependent on the test mass mechanical properties. For this reason, it is compulsory to use high optical and mechanical quality test mass materials in the advanced interferometer detectors. Fused silica has been used for test masses in detectors, while sapphire has been planned to be used for test mass substrates in the proposed Large-scale Cryogenic Gravitational-wave Telescope (LCGT) project. Other materials, such as calcium fluoride (CaF2), are also attractive, especially for cryogenic detectors. However, for the state-of-theAbstract II art facilities, it is difficult to manufacture very uniform, defect-free, inhomogeneity-free, high-quality, and large-size samples. Thus, the qualities of sapphire and calcium fluoride single crystal samples were investigated and evaluated, to ensure that they have suitable properties for use in interferometer detectors, i.e. with an adequately low level of imperfections, but also with high mechanical quality factor (Q-factor). This thesis describes research done in the endeavour to investigate bulk defects or inhomogeneities in test masses, as well as their induced thermal distortions, which appear at a high optical power in Laser Interferometric Gravitational-wave Detectors. An Automatic Rayleigh Scattering Mapping System (ARSMS) to examine the optical property of large-size test masses is described. This ARSMS enables quantitative high-resolution 3D mapping of defects or inhomogeneities in optical materials. The measured 3D defect distribution mapping of optical materials can assist in the design of suitable configurations of test masses in high optical power interferometers. In addition, a very sensitive Hartmann wavefront sensor was used to actively monitor the thermal distortions due to bulk and coating absorption in test masses. A very strong thermal distortion in these test masses was observed in the Gingin facility, demonstrating that thermal distortions could be a critical issue in advanced interferometer detectors. A negative thermo-optical coefficient material, to be used in a thermal distortion compensation method, was investigated for the compensation of very localised distortions due to imperfections. This thesis also includes experimental and theoretical studies of the scattering, absorption, and birefringence mechanisms, thermal distortion effects, and optimal compensation methods for test masses.

Paper discusses the expected uncertainty of orbital parameters of binary stars as measured by the space-based gravitational wave observatory LISA (Laser Interferometer Space Antenna) and how the inclusion of spin in the model of the binary stars affects the uncertainty. The uncertainties are found by calculating the received gravitational wave from a binary pair and then performing a linear least-squares parameter estimation. The case of a 1500 solar mass black hole that is 20 years from coalescing with a 1000 solar mass black hole--both of which are 50 x 10^6 light years away--is analyzed, and the results show that the inclusion of spin has a negligible effect upon the angular resolution of LISA but can increase the accuracy in mass and distance measurements by factors of 15 and 65, respectively.

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.

En septembre 2015, le détecteur LIGO a permis la première observation directe d'ondes gravitationnelles. Ce détecteur terrestre, tout comme le détecteur européen VIRGO, est basé sur des technologies purement optiques. Ces instruments sont extrêmement sensibles autour de 100 Hz mais ils sont limités en dessous de quelques dizaines de Hertz par différentes sources de bruit (bruit sismique, bruit newtonien...) qui ne sont pas distinguables de l'effet du passage d'une onde gravitationnelle.Le principe du projet MIGA (Matter wave – laser based Interferometer Gravitation Antenna) est de coupler un interféromètre optique avec plusieurs interféromètres atomiques séparés spatialement afin d'être sensible aux ondes gravitationnelles à plus basse fréquence (typiquement autour d'un Hertz). Les atomes froids sont lancés en configuration fontaine et sont séparés, réfléchis et recombinés par des impulsions laser effectuées dans une cavité optique de 300 m de long. Ces impulsions bénéficieront du gain optique intrinsèque au résonateur, leur permettant d'atteindre la puissance nécessaire à la réalisation de transitions de Bragg d'ordre élevé, augmentant ainsi la sensibilité des interféromètres atomiques. Chaque interféromètre mesure le champ gravitationnel local et les vibrations des miroirs. Le bruit sismique est donc rejeté dans le cas de mesures différentielles et en reconstruisant spatialement le champ gravitationnel, on pourra différencier le signal dû aux ondes gravitationnelles, qui est un pur gradient à l'échelle de l'instrument, du bruit newtonien qui a une signature spatiale.Les cavités de 300 m seront installées au LSBB (Laboratoire Souterrain Bas Bruit) à Rustrel, où l'antenne MIGA pourra bénéficier d'un environnement remarquablement calme. Cet instrument permettra de cartographier le champ gravitationnel du site, ce qui sera d'un grand intérêt pour l'étude géologique du massif karstique.Dans le cadre de ce projet, nous réalisons au LP2N une expérience préliminaire dont l'objectif est de générer un interféromètre de 87Rb en cavités en configuration de fontaine atomique. Cet instrument utilise une nouvelle architecture de résonateurs optiques demi-dégénérés afin de manipuler les atomes de façon cohérente avec des impulsions de Bragg. / In September 2015, the LIGO detector realized the first direct observation of gravitational waves. This ground-based detector, as well as the European detector VIRGO, is based on purely optical technologies. These instruments are extremely sensitive around 100 Hz but they are limited below few tens of Hertz by several sources of cavity length noise (seismic noise, Newtonian noise...) that mimic the effect of a gravitational wave.The idea of the MIGA (Matter wave-laser based Interferometer Gravitation Antenna) is to couple an optical interferometer with several atom interferometers spatially separated to be sensitive to gravitational waves at lower frequencies (typically around 1 Hz). The cold atoms are launched in a fountain configuration and are then split, deflected and recombined by laser pulses generated in a 300 m long optical cavity. These laser pulses will benefit from the intrinsic optical gain of the resonator, which will allow them to reach the needed power to generate high order Bragg transitions and to improve the sensitivity of the atom interferometers. Each interferometer measures the local gravitational field and the motion of the cavity. The seismic noise can be rejected by doing differential measurements and by reconstructing the spatial gravitational field, one can differentiate the gravitational wave signal, which is a pure gradient at the scale of our instrument, from the Newtonian noise that has a spatial signature.The 300 m long cavities will be implemented at the LSBB laboratory in Rustrel, where the antenna will benefit from an outstanding low noise environment. This instrument will allow to map the gravitational field of the site which will be of great interest for the geological study of the karstic massif.In the frame of this project, a preliminary experiment is currently under construction at the LP2N laboratory whose objective is to generate a 87Rb interferometer in a cavity in a atomic fountain configuration. This instrument uses a new architecture of half-degenerate optical resonators to manipulate coherently the atomic cloud with Bragg transitions.