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.

Le Centre Galactique abrite en son cœur un objet compact de plusieurs millions de masses solaires. L'hypothèse faite à l'heure actuelle est que cet objet serait un trou noir supermassif décrit par la relativité générale. L'instrument de seconde génération du Very Large Telescope Interferometer, GRAVITY, va permettre d'apporter des réponses quant à la réelle nature de cet objet. Grâce à sa précision astrométrique de 10 microsecondes d'angle, il va pouvoir sonder l'espace-temps en champ fort via l'observation des étoiles et du gaz situés à proximité de l'objet central.Au cours de ma thèse j'ai mis au point un modèle permettant de simuler les observations d'orbites d'étoiles de GRAVITY, l'objectif étant d'extraire à l'aide de celui-ci les paramètres fondamentaux du candidat trou noir central ainsi que les effets relativistes. Pour cela, j'ai utilisé le code de tracé de rayons GYOTO développé à l'Observatoire de Paris. Ce code permet de calculer des trajectoires d'étoiles et de photons obtenues en présence d'un objet compact. Il est alors possible de simuler les positions apparentes d'étoiles en orbite autour du Centre Galactique en calculant leur image relativiste.J'ai d'abord validé le calcul des trajectoires des photons effectué dans GYOTO. Grâce à des tests effectués en déflexion faible et forte, j'ai pu démontrer que GYOTO était hautement satisfaisant pour simuler les observations GRAVITY. En effet, j'ai montré que l'erreur sur le calcul des géodésiques de genre lumière était inférieure à environ 10^-2 microseconde d'angle, et cela même pour de grandes distances d'intégration.Je me suis ensuite intéressée à l'étude d'une étoile appelée S2 qui a contribué à fortement contraindre la masse de l'objet central. Sa proximité au Centre Galactique fait d'elle une cible idéale pour sonder l'espace-temps en champ fort. En particulier, j'ai estimé quels étaient les temps minimaux d'observation nécessaires pour détecter des effets relativistes à l'aide de mesures astrométriques et spectroscopiques obtenues sur l'étoile S2. Pour cela, j'ai mis en place plusieurs modèles d'orbites prenant en compte chacun un certain nombre d'effets relativistes. Le modèle le plus précis est obtenu en relativité générale complète avec le code GYOTO. Néanmoins, puisque l'étoile S2 est suffisamment éloignée de l'objet compact, ce modèle néglige certains effets de lentilles gravitationnelles telles que les images secondaires et l'amplification des images primaires. Par ailleurs, je me suis également intéressée à la contraindre du moment cinétique du candidat trou noir central avec cette étoile. En particulier, j'ai déterminé, grâce au modèle le plus précis mis en place ici, qu'il était possible de contraindre la norme et la direction du moment cinétique avec une incertitude d'environ 0,1 et 20 degrés, respectivement, et cela en considérant des observations obtenues sur trois périodes de S2 et des précisions de 10 microsecondes d'angle et 10 km/s.En vue de la possible détection d'étoiles plus proches du Centre Galactique par GRAVITY, j'ai développé un modèle prenant en compte les effets de lentilles négligés dans le modèle précédent. Néanmoins, afin de minimiser le temps de calcul demandé par celui-ci, j'ai déterminé une zone de l'espace dans laquelle il était tout de même possible d'utiliser ce dernier.Enfin, j'ai étudié l'influence de corps du Système Solaire sur les mesures astrométriques de GRAVITY, c'est-à-dire sur la séparation angulaire entre deux sources du Centre Galactique. Cette étude a montré que ces mesures différentielles n'étaient déviées que de quelques microsecondes d'angle par la perturbation gravitationnelle engendrée par le Soleil. Cependant, celles-ci sont modifiées de plusieurs centaines de microsecondes d'angle par l'effet d'aberration induit par le mouvement de la Terre par rapport aux sources du Centre Galactique. Il sera donc nécessaire de prendre en compte cet effet lors de l'interprétation des données obtenues par GRAVITY. / Decades of studies have demonstrated the presence of a compact object of several million solar masses at the center of the Galaxy. Nowadays, the assumption is that this compact object is probably a supermassive black hole described by general relativity. The second generation instrument at the Very Large Telescope Interferometer, GRAVITY, is expected to better constrain the nature of this central object. By using its astrometric accuracy of about 10 microarcseconds, it will probe spacetime in strong gravitational fields by observing stars and gas located near the compact object.During my PhD I have developed a stellar-orbit model in order to interpret the future GRAVITY observations. By using this model it will be possible to extract the central black hole candidate parameters and relativistic effects. To implement the model, I used the ray-tracing code GYOTO developed at Observatoire de Paris. This code allows computing star and photon trajectories obtained in the vicinity of a compact object. It is thus possible to simulate apparent positions of stars orbiting the Galactic Center by computing relativistic images.My work started by validating the photon trajectories computed in GYOTO. By doing tests in both weak- and strong-deflection limits, I have shown that the GYOTO code is highly qualified to simulate GRAVITY observations. Indeed, the error made on the photon trajectories is inferior to 10^-2 microarcsecond, even when integrating over large distances.Then, I was interested in studying a star called S2 that contributed to importantly constrain the mass of the central object. This star is the second closest star to the Galactic Center and has an orbital period of about 16 years. Nowadays, we do not know whether closer-in stars will be discovered by GRAVITY. It is thus important to extract as much information as possible from this star. In particular, I have estimated the minimal observation times needed to detect relativistic effects by using astrometric and spectroscopic measurements of S2. To do so, I have developed different stellar-orbit models taking into account a certain number of relativistic effects. The more accurate model is obtained by using the ray-tracing code GYOTO and considering all relativistic effects. However, as the S2 star is sufficiently far from the compact object, this model neglects certain gravitational lensing effects such as the secondary images and the primary images amplification. Besides, I was also interested in the possibility of constraining the angular momentum of the central black hole candidate with the S2 star. In particular, I have shown that with a model which does not use ray-tracing, the norm and the direction of the angular momentum can be constrained with an uncertainty of about 0.1 and 20 degrees, respectively, by using observations obtained during three periods of S2 and with accuracies reaching 10 microarseconds and 10 km/s.Since closer-in stars could be detected by GRAVITY, I have developed a more accurate stellar-orbit model taking into account the lensing effects neglected in the previous model. However, in order to minimize the computing time required by this model, I determined a volume in which it is possible to neglect both the secondary images and the primary images amplification.Finally, I have studied the impact of different components of the Solar System on astrometric positions measured by GRAVITY. This study has shown that those measurements are deviated by an amount of a few microarcseconds by the gravitational perturbation generated by the Sun. However, those apparent positions are shifted by several hundred microarcseconds by the aberration effect due to the movement of the Earth with respect to the Galactic Center. It is thus necessary to take into account this effect in future interpretations of GRAVITY observations.

This project contains an exposition of the basics of General Relativity up to the study of Gravitational Waves. The goal is to apply this theory to understand binary systems, how they generate gravitational waves and the energy they lose in doing so. Gravitational waves have been a topic of interest in relativity ever since their theoretical prediction in 1916. Now the interest in the subject has been renewed since LIGO's announcement of the first detection of gravitational waves, proving once again the power of General Relativity. This topic is very promising because of its implications in the future of astronomy and cosmology as a new method to obtain information about our universe.

In this thesis we look at mobile agent solutions to black hole search and related problems. Mobile agents are computational entities that are autonomous, mobile, and can interact with their environment and each other. The black hole search problem is for a team of these agents to work together to map or explore a graph-like network environment where some elements of the network are dangerous to the agents. Most research into black hole search has focussed on finding a single dangerous node: a black hole. We look at the problem of finding multiple black holes and, in the case of dangerous graph exploration, multiple black links as well. We look at the dangerous graph exploration problem in the network model. The network model is based on a normal static computer network modelled as a simple graph. We give an optimal solution to the dangerous graph exploration problem using agents that start scattered on nodes throughout the network. We then make the problem more difficult by allowing an adversary to delete links during the execution of the algorithm and provide a solution using scattered agents. In the last decade or two, types of networks have emerged, such as ad hoc wireless networks, that are by their nature dynamic. These networks change quickly over time and can make distributed computations difficult. We look at black hole search in one type of dynamic network described by the subway model, which we base on urban subway systems. The model allows us to look at the cost of opportunistic movement by requiring the agents to move using carriers that follow routes among the network's sites, some of which are black holes. We show that there are basic limitations on any solution to black hole search in the subway model and prove lower bounds on any solution's complexity. We then provide two optimal solutions that differ in the agents' starting locations and how they communicate with one another. Our results provide a small window into the cost of deterministic distributed computing in networks that have dynamic elements, but which are not fully random.

Comme introduction, nous présentons la formulation originale de la correspondance AdS/CFT, entre la théorie de Yang-Mills supersymétrique N = 4 avec groupe de jauge SU(N) et la théorie des supercordes de type IIB sur l'espace AdS5 x S5. Dans une première partie, nous montrons comment les ingrédients de la correspondance AdS/CFT peuvent être appliqués de manière phénoménologique à l'étude des systèmes de fermions fortement corrélés et présentons deux modèles fondamentaux, l'étoile à électrons et le supraconducteur holographique. Nous construisons un modèle holographique pour l'étude des systèmes de Bose-Fermi à densité finie et montrons que la présence simultanée de degrés de liberté bosoniques et fermioniques est favorisée à température nulle. En résolvant l'équation du mouvement d'un spineur test sur ces solutions, nous montrons que le système admet un grand nombre de surfaces de Fermi de type électron et/ou trou et un condensat scalaire chargé. Dans une seconde partie, nous nous intéressons à l'étude des solutions de trous noirs BPS asymptotiquement AdS4 dans la théorie de supergravité jaugée N = 2 en 4 dimensions. En utilisant les transformations de dualité dans un modèle STU simple, nous trouvons de nouvelles solutions de trous noirs BPS statiques et en rotation. / As an introduction, we present the original formulation of the AdS/CFT correspondence, between N = 4 Super Yang-Mills theory with gauge group SU(N) and type IIB string theory on AdS5 x S5. In a first part, we show how the ingredients of the AdS/CFT correspondence can be applied in a phenomenological way to study strongly correlated systems of fermions and present two fundamental models, the electron star and the holographic superconductor. We construct a holographic model for the study of Bose-Fermi systems at finite density and show that the simultaneous presence of bosonic and fermionic degrees of freedom is favoured at zero temperature. By solving the field equation of a probe spinor field in these solutions, we show that the system admits a large number of electron-like and/or hole-like Fermi surfaces and a charged scalar condensate. In a second part, we study asymptotically-AdS4 BPS black hole solutions in the N = 2 gauged supergravity theory. Using the duality transformations in a simple STU model, we find new static and rotating BPS black hole solutions.

<div>The development of novel passive techniques for vibration attenuation and control of broadband energy propagation through structural systems have been a major challenge in various complex engineering applications. These passive attenuation and control methodologies are necessary for the efficient performance of advanced lightweight aerospace and mechanical systems operating under extreme working conditions.</div><div><br></div><div>Acoustic Black Holes (ABH) have rapidly emerged as an effective approach to either dissipate or harvest mechanical energy in vibrating thin-walled structures. The characteristic dimension of an ABH, typically its diameter, is strictly connected to the occurrence of a cut-on frequency value below which the ABH is ineffective in absorbing the incoming wave. From a general perspective, lower the cut-on frequency, larger the ABH diameter needed to absorb the incoming wave. Design and manufacturing constraints of the host structure impose stringent limitations on the maximum ABH diameter and hence, limiting the lowest achievable cut-on frequency. The combination of these factors typically result in the poor energy extraction performance at low frequencies.</div><div><br></div><div>This thesis proposes the concept and explores the performance of an intentional nonlocal design for periodic grids of ABHs embedded in thin plates (referred to as ABH metastructures). The nonlocal design is conceived with the twofold objective of lowering the cut-on frequency of the ABH grids and extending the operating frequency range so as to achieve broadband performance. Different nonlocal designs are presented and their dynamic performances are investigated using numerical models. As opposed to the traditional material nonlocality, this thesis introduces nonlocal effects using an intentionally tailored geometric approach. A secondary layer is connected to the load-bearing ABH metastructure base, whose dynamic properties are sought to be controlled.</div><div><br></div><div>A semi-analytical model is also presented in order to characterize the role of nonlocality on the dispersion behavior and its effect on the broadband dynamic response. In linear elasticity, material nonlocality is mathematically represented by a spatially varying attenuation function. As the nonlocal model developed in this thesis follows geometric nonlocality approach, the required nonlocal attenuation factor is found to have a spatial as well as a temporal dependence. The analytical nonlocal constitutive relations in conjunction with the numerically obtained stress-strain parameters are used to identify the dynamic attenuation factor for the nonlocal ABH metastructure. The results provide substantial theoretical and numerical evidence of the potential of engineered nonlocal ABH design as an efficient ultra-low frequency passive attenuation technique for lightweight structures.</div>

Vision of a fictitious device that absorbs and keep matter content 7,2m3.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23707号 / 理博第4797号 / 新制||理||1687(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)准教授 上田 佳宏, 教授 嶺重 慎, 准教授 岩室 史英 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

An investigation into open problems related to black hole evaporation in the semi-classical framework, concerning the existence of quantum field theories on spacetimes modelling evaporating black holes as well as the existence of black hole solutions to the semi-classical Einstein equations. / Eine Untersuchung offener Probleme zur Verdampfung schwarzer Löcher im semi-klassischen Modell, bezüglich der Existenz von Quantenfeldtheorien auf Raumzeiten, die verdampfende schwarze Löcher beschreiben, sowie der Existenz von Lösungen der semi-klassischen Einstein Gleichungen, welche schwarze Löcher darstellen.

Axions are one of the best-motivated particles beyond the standard model of particle physics and a promising candidate for dark matter. Through the superradiant instability, axions can extract a significant amount of rotational energy from spinning black holes resulting in dense axion clouds. These axion clouds can imprint themselves on the spin of the black hole and even emit detectable gravitational waves, making them very potent tools in the search for axions. The considerable number of axions present in these clouds can also compensate for the weak coupling between the axion and the standard model particles. However, the interaction between the cloud and the astrophysical plasma that the black hole accretes is often assumed to be negligible. In this thesis, we examine this assumption by studying the interaction between the astrophysical plasma and the axion cloud to determine if it can cause any significant effects.  We find no new gravitational signatures and can conclude that the interaction is not effective enough to halt the evolution of the cloud. Therefore, the main focus of this work is the emitted low-frequency photons that the axions convert into through the interaction. We find that the emission from systems with typical accretion rates can reach up to 10^14 W and is most efficient around fast-spinning stellar black holes that accrete spherically without an accretion disk. However, we conclude that most of this emission will quickly be reabsorbed into the plasma and not cause any detectable signals.  We also study resonant conversion of axions, which can occur when the plasma frequency is comparable to the axion mass. We find that the low accretion rates that enable this are reachable around isolated stellar-mass black holes that travel rapidly through low-density regions of space. In these systems, the luminosity can reach 10^25 W, and possibly even higher if we include stimulation effects. We can, therefore, conclude that a population of fast-traveling isolated black holes can pose a new tool in the search for axions. / Axioner är en av de bäst motiverade partiklarna bortom standardmodellen för partikelfysik och en lovande kandidat för mörk materia. Genom superstrålning kan axioner extrahera en signifikant mängd rotationsenergi från svarta hål vilket kan resultera i täta axionmoln. Dessa axionmoln kan ge avtryck genom deras påverkan på spinnet hos svarta hål och till och med avge detekterbara gravitationsvågor. Detta gör axionmoln till kraftfulla verktyg i sökandet efter axioner. Den stora mängd axioner som dessa moln består av kan också kompensera för den svaga växelverkan mellan axionerna och partiklarna från standardmodellen. Växelverkan mellan molnet och den astrofysikaliska plasmat som det svarta hålet ackumulerar från omgivningen antas ändå ofta vara försumbar. I denna rapport undersöker vi detta antagande genom att studera växelverkan mellan den astrofysikaliska plasmat och axionmolnet för att avgöra om den kan orsaka några observerbara effekter. Vi finner inga nya gravitationella effekter och kan dra slutsatsen att växelverkan inte är tillräckligt effektiv för att påverka utvecklingen av axionmolnet. Därför är huvudfokus i detta arbete utstrålningen av de fotoner som resulterar från växelverkan. Vi finner att emissionen från system med typiska ackretionshastigheter kan nå upp till 10^14 W och är mest effektiv kring svarta hål med låg massa och högt spinn som ackumulerar sfäriskt utan att bilda en ackretionsskiva. Vi drar dock slutsatsen att det mesta av denna emission snabbt kommer att återabsorberas i plasmat och inte orsaka några detekterbara signaler. Vi studerar även konvertering av axioner via resonans, vilket kan inträffa när plasmafrekvensen är jämförbar med massan hos axionerna. Vi finner att de låga ackretionshastigheterna som möjliggör detta kan nås runt isolerade svarta hål som färdas snabbt genom delar av rymden med låg omgivande densitet. I dessa system kan luminositieten nå 10^25 W, och möjligen ännu högre om vi inkluderar stimuleringseffekter. Vi kan därför dra slutsatsen att en population av isolerade svarta hål med hög hastighet kan potentiellt användas i sökandet efter axioner.