As a non-linear theory of space-time, general relativity deals with interesting dynamical systems which can be expected more prone to chaos than their Newtonian counter-parts. In this thesis, we study the dynamics of time- like geodesics in the static and axisymmetric field of a Schwarzschild black hole surrounded, in a concentric way, by a massive thin disc or ring. We reveal the rise (and/or decline) of geodesic chaos in dependence on parameters of the sys- tem (the disc/ring mass and position and the test-particle energy and angular momentum), (i) on Poincaré sections, (ii) on time series of position and their power spectra, (iii) by applying two simple yet powerful recurrence methods, and (iv) by computing Lyapunov exponents and two other related quantifiers of or- bital divergence. We mainly focus on "sticky" orbits whose different parts show different degrees of chaoticity and which offer the best possibility to test and compare different methods. We also add a treatment of classical but dissipative system, namely the evolution of a class of mechanical oscillators described by non-standard constitutive relations.

Study of light rays (light world lines) plays a significant role in many of astro- physical applications. Light rays are mainly studied in terms of so-called grav- itational lensing. However, the majority of studies are mainly focused on light propagation in vacuum. If the refractive and dispersive medium characterised by refractive index n is considered, effects occurring due to the medium presence need to be taken into account, which significantly complicates the problem. In the present thesis, rays propagating through simple refractive and dispersive systems, such as plane differentially sheared medium, are studied. In order to simplify the problem, the Hamiltonian equations of motion are used. The ray trajectories in the vicinity of Kerr black hole as well as accessible regions for the rays are also studied. Radial variation of the medium velocity is considered. Due to the recent increase of publications focused on the gravitational lensing in plasma, a detailed review summarizing the results obtained recently is included. 1

An accretion torus is an important astrophysical phenomenon which is be- lieved to account for various features of mass inflow and release of radiation on diverse scales near stellar-mass as well as supermassive black holes. When the stationary torus is perturbed it starts to oscillate and once some part of the torus overflows the closed equipotential surface, defined by the stationary solution, this material is accreted or ejected. These oscillations reveal both spacetime properties and the intrinsic characteristics of the torus model. We study the oscillation and accretion properties of geometrically thick accretion tori using general relativistic magnetohydrodynamic simulations. Assuming axial symmetry these simulations are restricted to 2-D approximation. We discuss the impact of the presence of the large scale magnetic field and the profile of the specific angular momentum on the oscillation properties and on the accretion flow motion. 1

Cette thèse présente deux tests d'invariance de Lorentz, réalisés dans le cadre de l'Extension du Modèle Standard (SME). Le premier a pour objectif une recherche de violation dans le secteur SME de la matière, grâce aux données d'une horloge à atomes froids de 133Cs. La recherche de variations de la fréquence de transition hyperfine de cet atome a permis de contraindre plusieurs coefficients SME liés aux protons et aux neutrons, avec une sensibilité améliorant jusqu'à 12 ordres de grandeur les limites actuelles sur ces derniers. Le second test a été réalisé grâce aux données de la mission spatiale MICROSCOPE, en vol depuis le 25 avril 2016, qui a pour but de tester le Principe d'Équivalence faible avec une précision de l’ordre de 10−15 sur le paramètre d'Eötvös. Nous avons utilisé les mesures MICROSCOPE pour contraindre des violations d'invariance de Lorentz dues à un couplage entre matière et gravitation, en recherchant des variations de l'accélération relative de deux masses d'épreuve selon l'orientation de l'axe sensible de l'instrument, un double accéléromètre électrostatique. Les premiers résultats, obtenus grâce à l'analyse de cinq sessions de mesures, ont déjà démontré une amélioration jusqu'à 4 ordres de grandeur des contraintes sur deux coefficients du secteur SME de la matière couplée à la gravitation. / This thesis presents two Lorentz invariance tests, performed within the Standard Model Extension framework (SME). The first one is a search for a violation in the matter sector of the SME, using data from a cold atom clock. The search for variations in the hyperfine transition frequency of 133Cs allowed us to constrain several SME coefficients related to protons and neutrons, with a sensitivity improving by up to 12 orders of magnitude the current best laboratory limits on these coefficients. The second test was carried out using the data from the MICROSCOPE space mission, in flight since April 2016, which is intended to test the Weak Equivalence Principle (WEP) with an accuracy of 10−15 on the Eötvös parameter. In this experiment, a coupling between matter and gravitation could lead to Lorentz violation signals and therefore to variations in relative acceleration of two test masses depending on the satellite orientation. The relative acceleration is measured by a differential electrostatic accelerometer. The first results, obtained through the analysis of five sessions, have already demonstrated an improvement of up to 4 orders of magnitude of the constraints on two coefficients of the SME sector of matter-gravity couplings.

The aim of this report is to explore different models of cosmology, depending on components as matter, radiation and dark energy. To be able to investigate the behaviour and age of these model universes, it is necessary to solve the Friedmann equation. Therefore a substantial part of this thesis is a study of general relativity, including mathematical tools as Riemannian geometry and the concept of curved space-time. / Denna rapport ämnar att utforska olika kosmologiska modeller beroende på innehåll som materia, strålning och mörk energi. För att undersöka beteendet och åldern av dessa modellerade universa så är det nödvändigt att lösa Friedmann-ekvationen. Därför ägnas en betydande del av detta arbete åt att studera allmän relativitetsteori, med matematiska verktyg som Riemanngeometri och konceptet krökt rum-tid.

Kerr metric is one of the most well-known and useful exact solutions of Einstein equations. We study various geometric properties of the Kerr spacetime in order to gain intuition for its spatial shape. In the review part we summarize basic features of the Kerr geometry, we write down Carter equations for geodesic motion in the Kerr spacetime, and we introduce kinematic characteristics of time-like and light-like congruences, such as expansion, shear and twist. In the second part of the thesis we calculate scalars for acceleration, expansion, shear and twist - and plot the corresponding "equipotential" surfaces - for several privi- leged congruences, namely the Carter observers, the static observers, the zero-angular- momentum observers, the principal null congruence and the recently found non-twisting null congruence(s). We also draw surfaces radially equidistant from the horizon and sur- faces spatially orthogonal to the PNC and to the twist-free congruences, as well as the surfaces of constant energy and redshift for the important time-like congruences. 1

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20176号 / 理博第4261号 / 新制||理||1612(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 田中 貴浩, 教授 川合 光, 教授 向山 信治 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20903号 / 理博第4355号 / 新制||理||1625(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々木 節, 教授 柴田 大, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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The first detection of a gravitational wave (GW) enabled our observation of the Universe through a revolutionary messenger and unveiled phenomena that are occurring in a range of very strong gravitational fields and relativistic velocities. These physical regimes, previously inaccessible to humankind, can now be studied. In particular, the discoveries of an unexpected population of stellar-mass binary black holes (BBH), and unexpected masses for binary neutron star (BNS) components have both pointed to new astrophysics, and to unprecedented tests of the general relativity theory. This thesis focuses on the development of a new method of gravitational wave data analysis, aiming to investigate weak features in the proximity to well-identified BBH merger signals. The method is based on a dedicated version of coherentWaveBurst (cWB), an unmodelled gravitational waves transient search algorithm, developed in the LIGO Scientific Collaboration (LSC) and Virgo Collaboration and widely used on LIGO-Virgo-KAGRA (LVK) data. CoherentWaveBurst relies on the coherent detection of an excess of energy inside the combined data of all the gravitational waves detectors inside the detectors network. Such excess of energy must pass several internal thresholds of the pipeline to be accepted as a possible gravitational wave candidate and these thresholds evaluate not only the strength of the signal with respect to the background noise but also how balanced is the energy distribution among the detectors of the network, its coherence, as well as other quantities whose purpose is to rule out possible outliers due to the presence of non-stationary noise. To develop such a method, it was decided to adopt as science case the search for echoes. In literature, it has been proposed that the gravitational radiation generated from a binary compact objects (CBCs) coalescence might display exotic characteristics if compared to the predicted one generated by black hole-black hole (BH-BH), neutron star-neutron star (NS-NS), or neutron star-black hole (NS-BH) binaries which are, for now, the only detected emitters of gravitational waves. Such differences arise from the proposal that the involved compact objects (COs) of the binary are not standard black holes but instead black hole mimickers called exotic compact objects (ECOs). If this is the case the gravitational wave signal generated from such a binary would display repeated gravitational wave pulses, of widely uncertain morphology, after the merger-ringdown phase of the gravitational signal. These repeated gravitational wave pulses are called echoes, one class of low energetic signals whose presence inside gravitational wave data, this new algorithm is searching for. The proposed data analysis methodology searching for echoes is agnostic over the properties of the predicted gravitational wave pulses emitted by an ECO binary. Indeed, the variety of theoretical alternatives to black holes is not converging over a well-defined post-merger-ringdown signal, each model has its own properties and characteristic features. Therefore, the possibility to investigate the morphological features of possible outliers in the post-merger phase of detected GW signals is fundamental in the process of inferring their nature. Having their morphology recovered without priors makes the proposed search more general than the variety of theoretical models of echoes. This procedure is tested over real data from past LIGO-Virgo observing runs (O1, O2, and O3), and the capability of the search in estimating the main morphological parameters of echoes, such as their arrival time, mean frequency, as well as the amplitude attenuation between subsequent pulses, is investigated. This work concludes that the current state-of-the-art methods and detectors find no evidence for echoes of any morphologies. Such a study extended to lower signal-to-noise ratio (SNR) the detectability of echoes associated with the public gravitational-wave transient catalog of BBH mergers released by the LIGO and Virgo Collaboration. It also sets best quantitative upper limits on the amplitude of low energy signals occurring after the merger-ringdown. To achieve these results, new post-processing tools are developed and optimised to detect and characterize possible energy excess inside a user-defined time window. This required the development of the code and to adapt the cWB infrastructure to the new working requirements which also involves a re-tuning of cWB itself. The optimization of the performances is based on off-source simulations for assessing the detection efficiency and false alarm probability of signal candidates.