This thesis reports on the recent results of a continuing, high-precision pulsar timing project, currently focused on the nearby, binary millisecond pulsar, PSR J0437_4715. Pulse arrival time analysis has yielded a remarkable series of constraints on the physical parameters of this system and evidence for the distortion of space-time as predicted by the General Theory of Relativity. Owing to the proximity of the PSR J0437_4715 system, relative changes in the positions of the Earth and pulsar result in both annual and secular evolution of the line of sight to the pulsar. Although the changes are miniscule, the effects on the projected orbital parameters are detectable in our data at a high level of significance, necessitating the implementation of an improved timing model. In addition to producing estimates of astrometric parameters with unparalleled precision, the study has also yielded the first three-dimensional orbital geometry of a binary pulsar. This achievement includes the first classical determination of the orbital inclination, thereby providing the unique opportunity to verify the shape of the Shapiro delay and independently confirm a general relativistic prediction. With a current post-fit arrival time residual RMS of 130 ns over four years, the unrivaled quality of the timing data presented herein may eventually contribute to the most stringent limit on the energy density of the proposed stochastic gravitational wave background. Continuing the quest for even greater timing precision, a detailed study of the polarimetry of PSR J0437_4715 was undertaken. This effort culminated in the development of a new, phase-coherent technique for calibrating the instrumental response of the observing system. Observations were conducted at the Parkes 64-m radio telescope in New South Wales, Australia, using baseband recorder technologies developed at York University, Toronto, and at the California Institute of Technology. Data were processed off-line at Swinburne University using a beowulf-style cluster of high-performance workstations and custom software developed by the candidate as part of this thesis.

I perform and analyse the first ever calculations of rotating stellar iron core collapse in {3+1} general relativity that start out with presupernova models from stellar evolutionary calculations and include a microphysical finite-temperature nuclear equation of state, an approximate scheme for electron capture during collapse and neutrino pressure effects. Based on the results of these calculations, I obtain the to-date most realistic estimates for the gravitational wave signal from collapse, bounce and the early postbounce phase of core collapse supernovae. I supplement my {3+1} GR hydrodynamic simulations with 2D Newtonian neutrino radiation-hydrodynamic supernova calculations focussing on (1) the late postbounce gravitational wave emission owing to convective overturn, anisotropic neutrino emission and protoneutron star pulsations, and (2) on the gravitational wave signature of accretion-induced collapse of white dwarfs to neutron stars. / Ich präsentiere die ersten Computer-Simulationen des rotierenden Kollapses stellarer Eisenkerne, die in der {3+1}-Zerlegung der Allgemeinen Relativitätstheorie durchgeführt werden und Vorsupernova-Sternmodelle aus Sternentwicklungsrechnungen, eine heiße nukleare Zustandsgleichung und ein näherungsweises Verfahren zur Beschreibung des Elektroneneinfangs enthalten und Neutrinodruck-Effekte berücksichtigen. Basierend auf den Ergebnissen dieser Rechnungen erhalte ich die zur Zeit realistischsten Vorhersagen für das Gravitationswellensignal der Kollaps, Abprall, Abkling und frühen Nach-Abprallphase einer Kern-Kollaps-Supernova. Neben den {3+1} Simulationen diskutiere ich newtonsche axisymmetrische Kern-Kollaps-Supernova-Simulationen mit Schwerpunkten auf: (1) der Gravitationswellenabstrahlung in der späten Nach-Abprallphase durch Konvektionsströmungen, anisotropische Neutrinoemission und Proto-Neutronenstern Pulsationen und (2) der Gravitationswellensignatur des Kollapses weißer Zwergsterne zu Neutronensternen, der durch Akkretion eingeleitet wird.

In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.

A written report of a paper titled Holographic dual of collimated radiation by Veronika E. Hubeny where a new and easier method is proposed to estimate the “radiation due to an accelerated quark in a strongly coupled medium”. The method is able to reproduce the results from an earlier paper without the need of solving the linearized Einstein equations but by way of calculating geodesics in AdS using the AdS/CFT correspondence and the gravitational dual of the quark being a string. A quick introduction to synchrotron radiation and general relativity is given after which the AdS/CFT correspondence is introduced along with the results and method of V. Hubeny. / A bachelor thesis in theoretical physics.

<p>We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus proving the Riemannian positive mass theorem in this case. If the graph has convex horizons, we also prove the Riemannian Penrose inequality by giving a lower bound to the boundary integrals using the Aleksandrov-Fenchel inequality. We also prove the ZAS inequality for graphs in Minkowski space. Furthermore, we define a new quasi-local mass functional and show that it satisfies certain desirable properties.</p> / Dissertation

<p>In general relativity, the nature of mass is non-local. However, an appropriate def-inition of mass at a quasi-local level could give a more detailed characterization ofthe gravitational field around massive bodies. Several attempts have been made tofind such a definition. One of the candidates is the Hawking mass. This thesispresents a method for calculating the spin coefficients used in the expression for theHawking mass, and gives a closed-form expression for the Hawking mass of ellipsoidal2-surfaces in Minkowski spacetime. Furthermore, the Hawking mass is shown to havethe correct limits, both in Minkowski and Schwarzschild, along particular foliationsof leaves approaching a metric 2-sphere. Numerical results for Schwarzschild are alsopresented.</p>

The influence of matter described by the Vlasov equation, on the evolution of anisotropy in the spatially-homogeneous universes, called the Bianchi cosmologies, is studied. Due to the spatial-homogeneity, the Einstein equations for each Bianchi Type are reduced to a set of coupled ordinary differential equations, which has Hamiltonian form with the metric components being the canonical coordinates. In the vacuum Bianchi cosmologies, it is known that a curvature potential, which comes from the symmetries of the three-dimensional Lie groups, determines the basic properties of the evolution of anisotropy. In this work, matter potentials are constructed for Vlasov matter. They are obtained by first introducing a new matter action principle for the Vlasov equation, in terms of a conjugate pair of functions, and then enforcing the symmetry to obtain a reduction. This yields an expression for the matter potential in terms of the phase space density, which is further reduced by assuming cold streaming matter. Some vacuum Bianchi cosmologies and Type I with Vlasov matter are compared. It is shown that the Vlasov-matter potential for cold streaming matter results in qualitatively distinct dynamics from the well-known vacuum Bianchi cosmologies. / text

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The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73].