The radiative mechanism responsible for the prompt gamma-ray burst (GRB) emission remains elusive. For the last decade, optically thin synchrotron emission from shocks internal to the GRB jet appeared to be the most plausible explanation. However, the synchrotron interpretation is incompatible with a significant fraction of GRB observations, highlighting the need for new ideas. In this thesis, it is shown that the narrow, dominating component of the prompt emission from the bright GRB090902B is initially consistent only with emission released at the optically thick jet photosphere. However, this emission component then broadens in time into a more typical GRB spectrum, which calls for an explanation. In this thesis, a previously unconsidered way of broadening the spectrum of photospheric emission, based on considerations of the lateral jet structure, is presented and explored. Expressions for the spectral features, as well as polarization properties, of the photospheric emission observed from structured, relativistic jets are derived analytically under simplifying assumptions on the radiative transfer close to the photosphere. The full, polarized radiative transfer is solved through Monte Carlo simulations, using a code which has been constructed for this unique purpose. It is shown that the typical observed GRB spectrum can be obtained from the photosphere, without the need for additional, commonly assumed, physical processes (e.g. energy dissipation, particle acceleration, or additional radiative processes). Furthermore, contrary to common expectations, it is found that the observed photospheric emission can be highly linearly polarized (up to $\sim 40 \, \%$). In particular, it is shown that a shift of $\pi/2$ of the angle of polarization is the only shift allowed by the proposed model, consistent with the only measurement preformed to date. A number of ways to test the theory is proposed, mainly involving simultaneous spectral and polarization measurements. The simplest measurement, which tests not only the proposed theory but also common assumptions on the jet structure, involves only two consecutive measurements of the angle of polarization during the prompt emission. / <p>QC 20131204</p>

This thesis begins by introducing the concept of a rigid quasilocal frame (RQF) as a geometrically natural way to define an extended system in the context of the dynamical spacetime of general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume with the rigidity conditions that the congruence of worldlines is expansion-free (the ``size'' of the system is not changing) and shear-free (the ``shape'' of the system is not changing). We demonstrate that this frame exists in flat and arbitrary curved spacetimes and, moreover, exhibits the full six motional time-dependent degrees of freedom we are familiar with from Newtonian mechanics. The latter result is intimately connected with the fact that a spatial slice through the RQF - having a two-sphere topology - always admits precisely six conformal Killing vector (CKV) fields (three boosts and three rotations) associated with the action of the Lorentz group on a two-sphere. These CKVs, along with the four-velocity of observers on the RQF, are then used to quasilocally define the energy, momentum, and angular momentum inside an RQF without relying on the pre-general relativistic practice of appealing to spacetime symmetries. These quasilocal definitions for energy, momentum, and angular momentum also involve replacing the local matter-only stress-energy-momentum (SEM) tensor with the Brown-York matter plus gravity boundary SEM tensor. This allows for the construction of completely general conservation laws which describe the changes in a system in terms of fluxes across the boundary. Furthermore, since an RQF is a congruence with zero expansion and shear only relevant fluxes appear in these conservation laws - that is, fluxes due merely to changes in the size or shape of the boundary are eliminated. These resulting fluxes are simple, exact, and quantified in terms of operationally-defined geometrical quantities on the boundary and we show that they explain at a deeper level the mechanisms behind gravitational energy and momentum transfer by way of the equivalence principle. In particular, when we accelerate relative to a mass, the energy changes at a rate proportional to our acceleration times the momentum (and we propose an exact gravitational analogue of the electromagnetic Poynting vector to capture this idea). Similarly, the momentum of that object changes at a rate proportional to our acceleration times the energy. This new insight has fascinating consequences for how we should understand everyday occurrences like a falling apple - that is, the change in energy of the apple involves frame dragging while the change in momentum involves extrinsic curvature effects near the apple. Our naive general relativistic intuition tells us that these quantities should be so tiny that they should be negligible and, indeed, they are tiny but they are multiplied by huge numbers to give rise to macroscopic effects. This is how general relativity universally explains the transfer of energy and momentum but we needed rigid quasilocal frames to uncover this beautiful property of nature. Using the RQF formalism we also investigate a variety of specific problems. In particular, while looking at time-dependent rotations we discover that the reason Ehrenfest's rigid rotating disk paradox has gone unsolved for so long is that rotation introduces a subtle non-locality in time. By this we mean that, in order to maintain rigidity while undergoing time-dependent rotation, one needs to know, not only the instantaneous rotation rate, but the entire history of the motion. This makes it impossible to keep a volume of observers rigid but is doable with an RQF. We also consider RQFs in the small-sphere limit to derive many of our results and one example with particularly interesting consequences involves Bell's spaceship accelerating through an electromagnetic field. Here, we show that the change in electromagnetic energy inside the spaceship is made up of two pieces: the usual electromagnetic Poynting flux accounts for half the change while the gravitational Poynting vector equally contributes to make up the other half. This means that electromagnetism in flat spacetime generically does not tell you what is actually going on. Rather, the curvature due to the electromagnetic field necessitates a fully general relativistic treatment to get the whole story. We also use the RQF linear momentum conservation law in the context of stationary observers and fields to derive, for the first time, an exact fully general relativistic analogue of Archimedes' law. In essence, this law demonstrates that the weight of the matter and gravitational fields contained in a finite region of space is supported by the stresses (buoyant forces) acting on the boundary of that region. Furthermore, in a post-Newtonian approximation, we derive a simple set of quasilocal conservation laws which describe non-relativistic systems bound by mutual gravitational attraction. In turn, we use these laws to obtain expressions for the rates of gravitational energy and angular momentum transfer between two tidally interacting bodies - that is, the tidal heating and tidal torque - without the need to define unphysical pseudotensors. Moreover, the RQF approach explains these transfers of energy and momentum again, not as the difference of forces acting on a tidal bulge, but instead more fundamentally in the language of the equivalence principle in terms of ``accelerations relative to mass''. Throughout this work we demonstrate that the RQF approach always gives very simple, geometrical descriptions of the physical mechanisms at work in general relativity. Given that this approach also includes both matter and gravitational energy, momentum, and angular momentum and does not rely on spacetime symmetries to define these quantities, we argue that we are seeing here strong evidence that the universe is actually quasilocal in nature. We are really deeply ingrained with a local way of thinking, so shifting to a quasilocal mindset will require great effort, but we contend that it ultimately leads to a deeper understanding of the universe.

Structures within general relativity are examined. The differences between man-made structures and those predicted by the Einstein differential equations are very subtle. Exotic structures such as the Godel Universe and the Gott cosmic string are examined with emphasis on closed time-like curves. Newtonian models are seen to also have an exotic aspect in that a vast halo consisting of unknown matter dominates the galaxy. We introduce a model for galaxies based on a general relativity framework with the goal of excluding such artifacts from the system while describing the flat-rotation curves. Structures within this model were speculated to be exotic but after close scrutiny, their nature is shown to be benign. Numerical approaches are applied to model four galaxies: The Milky Way, NGC 3031, NGC 3198 and NGC 7331. Density and mass are deduced from these models and compared to the Newtonian models. Within the visible/HI region, there is 30% reduction in total mass. Extending the model to 10 times beyond the HI region using various fall-off scenerios, it is shown that there is only modest increase of the accumulated mass. In comparison to the Newtonian approach to galactic dynamics, the massive halos are not required to account for the flat velocity profiles.

In this thesis, we discuss a geometric construction analogous to the Ward correspondence for the KP equations. We propose a Dirac operator based on the inverse scattering transform for the KP-II equation and discuss the similarities and differences to the Ward correspondence. We also consider the KP-I equation, describing a geometric construction for a certain class of solutions. We also discuss the general inverse scattering of the equation, how this is related to the KP-II equation and the problems with describing a single geometric construction that incorporates both equations. We also consider the Davey-Stewartson equations, which have a similar behaviour. We demonstrate explicitly the problems of localising the theory with generic boundary conditions. We also present a reformulation of the Dirac operator and demonstrate a duality between the Dirac operator and the first Lax operator for the DS-II equations. We then proceed to generalise the Dirac operator construction to generate other integrable systems. These include the mKP and Ishimori equations, and an extension to the KP and mKP hierarchies.

Includes bibliographical references (leaves 168-179). / xiii, 179 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Finds that the post-Newtonian approximation seems to be a better approximation of the general relativistic theory than the standard Newtonian theory. / Thesis (Ph.D.)--Adelaide University, Dept. of Physics and Mathematical Physics, 2001

Thesis (M.A.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains iv, 233 p. Includes abstract. Includes bibliographical references (p. 205-233).

Thesis (Ph. D.)--University of Notre Dame, 2008. / Thesis directed by Don Howard for the Department of History and Philosophy of Science. "July 2008." Includes bibliographical references (leaves 196-233).

Thesis (PhD)--Montana State University--Bozeman, 2009. / Typescript. Chairperson, Graduate Committee: Neil J. Cornish. Includes bibliographical references (leaves 137-140).

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Richard Matzner. Vita. Includes bibliographical references. Available also from UMI company.

Thesis (M.S.)--Ohio University, June, 2002.