Isolated and Dynamical horizons are used to generate boundary conditions upon the lapse and shift vectors. Numerous results involving the Hamiltonian of General relativity are derived, including a self-contained derivation of the Hamiltonian equations of general relativity using both a direct 'brute force' method of directly computing Lie derivatives, as well as the standard Hamil- tonian approach. Conclusions are compared to numerous examples, including the Kerr, Schwarzschild-De Sitter, McVittie, and Vaiyda spacetimes. / text

Static, spherically-symmetric particle-like solutions to the coupled Einstein-Dirac and Einstein-Dirac-Maxwell equations have been studied by Finster, Smoller and Yau (FSY). In their work, FSY left the fermion mass as a parameter set to ±1. This thesis generalises these equations to include the Higgs field, letting the fermion mass become a function through coupling, μ. We discuss the dynamics associated with the Higgs field and find that there exist qualitatively similar solutions to those found by FSY, with well behaved, non-divergent metric components and electrostatic potential, close to the origin, going over to the point-particle solutions for large r; the Schwarzschild or Reissner-Nordström metric, and the Coulomb potential. We then go on to discuss an alternative gravity theory, conformal gravity, (CG), and look for solutions of the CG equations of motion coupled to the Dirac, Higgs and Maxwell equations. We obtain asymptotically nonvanishing, yet fully normalisable Dirac spinor components, resembling those of FSY, and, in the case where charge is included, non-divergent electrostatic potential close to the origin, matching onto the Coulomb potential for large r.

Exact solutions to Einstein's field equations in the presence of matter are presented. A one parameter family of interior solutions for a static fluid is discussed. It is shown that these solutions can be joined to the Schwarzschild exterior, and hence represent fluid spheres of finite radius. Contained within this family is a set of solutions which are gaseous spheres defined by the vanishing of the density at the surface. One such solution yields an analytic expression which corresponds to the asymptotic numerical solution of Oppenheimer and Volkoff for the degenerate neutron gas. These gaseous spheres have ratios of specific heats that lie between one and two in the vicinity of the origin, increasing outward, but remaining less than the velocity of light throughout.

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

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

This report presents a selfcontained derivation of Hawking radiation, and discusses the consequent information loss paradox.

Understanding the apparent accelerating expansion rate of the universe is a challenge for modern cosmology. One category of explanations is that we are using the wrong gravitational physics to study the observations. Our paradigmatic theory of gravity – Einstein’s theory of General Relativity – may be subsumed by a larger theory. This thesis develops a selection of tools for testing General Relativity and the numerous alternative theories of gravity that have been put forward. I advocate that an elegant and efficient way to test this space of theories is through the use of parameterized frameworks. Inspired by the Parameterized Post-Newtonian framework I develop a new formalism, the Parameterized Post-Friedmann formalism, that aims to unify the linear cosmological perturbation theory of many alternatives to General Relativity. Having introduced the Parameterized Post-Friedmann formalism and demonstrated its application via a suite of examples, I examine several issues surrounding parameterized tests of gravity. I first consider how the structure of a parameterization can influence the constraints obtainable from a given set of data. I then consider how to describe the growth of the large-scale structure of the universe in a parameterized manner. This leads to a convenient tool for calculating corrections to the growth rate of structure in modified theories, which can be used both with the Parameterized Post-Friedmann formalism or independently of it. I present forecasts for how well generalized deviations from General Relativity will be constrained by the next generation of galaxy surveys. Throughout, this thesis aims to take a synoptic approach to theories of modified gravity, rather than focussing on specific models. A question yet to be answered is whether this approach is realistic in practical terms. The final part of this thesis takes the first steps towards an answer.

Gamma-ray bursts (GRBs) are the mysterious, short and intense flashes of gamma-rays in the space, and are believed to originate from the rare, explosively devastating, stellar events that happens at cosmological distances. Enormous progress has been made from four decades of GRB research endeavor but the ultimate understanding of their origins has yet to arrive. Recently revealed features in their early afterglows broadened the opportunity space for exploration. We have carried out extensive studies on various physical processes in GRBs. We showed that the distribution of electrons' energy spectral index in GRBs and other relativistic sources is inconsistent with the prediction from the first-order Fermi theory of the shock particle acceleration. We investigated the photon scattering processes within the relativistic outflow that produces the GRB and calculated the resultant emission flux from it. We showed the scattering of the GRB prompt photons by the circum-burst dust, although an attractive possibility, can not explain the puzzling plateau component in the GRB afterglow light curve. We made meaningful constraint on the GRB prompt emission radius, R [greater-than or equal to] 10¹⁴, by studying the synchrotron self absorption for a small sample of bursts with good data. We showed that a late jet, which is thought to be producing the late X-ray flares in GRB afterglows, will produce detectable emissions from its interactions with other components in the explosive event of GRB, and identification of these emissions could verify the existence of the late jet and further prove the massive star origin of long-duration GRBs. / text

<p>Neutron stars are some of the most fascinating objects in Nature. Essentially all aspects of physics seems to be represented inside them. Their cores are likely to contain deconfined quarks, hyperons and other exotic phases of matter in which the strong interaction is the dominant force. The inner region of their solid crust is penetrated by superfluid neutrons and their magnetic fields may reach well over 10¹²Gauss. Moreover, their extreme mean densities, well above the densities of nuclei, and their rapid rotation rates makes them truly relativistic both in the special as well as in the general sense. This thesis deals with a small subset of these phenomena. In particular the exciting possibility of trapping of gravita-tional waves is examined from a theoretical point of view. It is shown that the standard condition <i>R</i> < 3<i>M</i> is not essential to the trapping mechanism. This point is illustrated using the elegant tool provided by the optical geometry. It is also shown that a realistic equation of state proposed in the literature allows stable neutron star models with closed circular null orbits, something which is closely related to trapped gravitational waves. Furthermore, the general relativistic theory of elasticity is reviewed and applied to stellar models. Both static equilibrium as well as radially oscillating configurations with elasticsources are examined. Finally, Killing tensors are considered and their applicability to modeling of stars is discussed</p>

The basic concept to be used in studying the question of one-particle interpretations of relativistic wave equations is that of observables and operator representations that are different from the more usual classically motivated observables and representations. In particular, the concept of a mean-position observable will be used to determine to what extent the one-particle "problems" can be resolved.