Jennifer Elayne Briscoe (Masters Thesis, December 2003,
Advisor: Kent Harrison
)

Abstract

For a good portion of the latter part of the twentieth century, many believed the universe to be open or flat-expanding yet asymptotically slowing down. There were some that ventured to theorize other fates for our universe, but an open or flat universe seemed the most likely picture at the time. In 1998, two separate supernova research team reported that their independent data sets indicated a recent accelerating expansion pf the universe, starting around 8.5 billion years ago. Observational data collected from sources other than supernovae told the same story. This started a deluge of research with many ideas about what could be causing this acceleration and the mathematics behind it. Several popular ideas have stood out in the almost five years since the supernova research teams reported their findings. Alan Guth’s inflationary theory was revisited to assist in modeling this acceleration. Einstein’s cosmological constant was among the first to be revisited, as well as use of a scalar field. The cosmological constant could also be identified with an asymptotically constant scalar field. Quintessence was also reintroduced by Steinhardt and colleagues as a field that interacts with matter and radiation. Brane theory, where the energy responsible for acceleration in the universe comes from another dimension in our universe, is described using M-theory, the latest version of string theory. I investigate the general plausibility of these, and conclude that all of the above are currently viable theories, and more refined data are needed to help settle which, if any, of our current theories is correct.

David W Neilsen (Masters Thesis, August 1995,
Advisor: Kent Harrison
)

Abstract

The Einstein field equations describing a stationary, axially symmetrical rigidly rotating, relativistic, perfect fluid are reduced with a similarity transformation to ordinary differential equations. A Lie-Backlund symmetry analysis is used to obtain the similarity variables. Approaches to a solution of the equations are discussed. A simple case allows the equations to be solved, yielding a non-rotating spacetime with Cartesian symmetry.

Shawn Young (Senior Thesis, May 1994,
Advisor: Kent Harrison
)

Abstract

Richard Clawson (Senior Thesis, May 1992,
Advisor: Kent Harrison
)

Abstract

David Wayne Halliday (PhD Dissertation, December 1992,
Advisor: Kent Harrison
)

Abstract

This paper develops a formalism for Dirac-like equations (linear complex differential equations, linear in all derivatives), allowing for general coordinate and “spin-space” (internal space) transformations. A correspondence principle is also developed by requiring solutions to the Dirac-like equations to be solutions to a Klein-Gordon equation that is likewise generally invariant. Through this treatment, previous generalizations of the Dirac equation are incorporated, and various aspects of these methods are analyzed. Furthermore, the Yang-Mills-like gauge fields allowed, or required, by the formalism are expressed, and found to be associated with much larger symmetries than most would desire, suggesting either there has been much greater symmetry breaking than expected, or else few of the particles we accept as fundamental really are. It is also found that unless the space-time is “parallelizable” )so there exist fields that are everywhere parallel transported into themselves, which is not generally the case), or some of the wave function components (and separately some of the Yang-mills fields) are independent, we cannot have the Dirac gamma operators commuting with the momentum operators, while simultaneously having a spin-space metric that is compatible with the Yang-Mills fields.

Edward F Weagel (Masters Thesis, August 1992,
Advisor: Kent Harrison
)

Abstract

Einstein’s field equations with a Bianchi type VII0 metric (anisotropic0 were solved numerically for both the case of an energy momentum tensor which included a scalar field, as well as for one that did not; this was done for a variety of different initial conditions. When the scalar field was included, inflationary solutions were readily obtained.

Costas J Papachristou (PhD Dissertation, August 1987,
Advisor: Kent Harrison
)

Abstract

Ira R. Rostron (PhD Dissertation, August 1970,
Advisor: Kent Harrison
)

Abstract

A theoretical study of some of the properties of neutron stars is made. The principal interest is in magneto hydrodynamic behavior in the presence of gravitational potentials and large magnetic fields. Expressions are derived from Maxwell’s equations, the energy equation, the momentum equation and the equation for electric charge in the presence of gravitational potentials. The relativistic equation of continuity and an equation of state are then selected to complete the necessary equations. Magneto hydrodynamic behavior is then considered it the static case and expressions are obtained for magnetic pressure, viscosity, magnetic energy and Poynting vector. Then wave behavior is considered in incompressible matter and in compressible matter. A dipole-like magnetic field is considered in the regions outside the neutron star. Finally, a general magnetic field is obtained for the regions outside and inside the star and the two fields are matched at the surface.

Harold Bird Hart (PhD Dissertation, January 1969,
Advisor: Kent Harrison
)

Abstract

A review of methods of deriving conservation laws for physical systems is carried out with particular emphasis on the symmetry method. Previous application of conservation laws to classical and relativistic theories, especially Einstein’s pseudo tensor, the Freud and Moller super potentials, and the Komar generator are derived. Two possible forms of the scalar-tensor Komar generator are discussed and application of these generators to the scalar-tensor Schwarzchild field yields two different results for the total energy both of which have been obtained previously by other methods. The symmetry properties of scalar-tensor theories are examined and a restriction of Killing’s equations is found which seems to have a physical significant.

Lloyd A Case (PhD Dissertation, January 1968,
Advisor: Kent Harrison
)

Abstract

A theoretical study is made of the evolution of one Petrov type of space-time into another (“Evolution” meaning the change of the Petrov type a point observer would consider his local space-time). This study is motivated by a desire to increase the present understanding of this invariant classification and thereby improve its use as a tool for understanding solutions to the field equations of general relativity. The study happens to involve a detailed consideration of discontinuities in space-time. From this study an algorithm is developed that many be used to test the evolution of any closed form solution of interest. An example of its use is included. Also a flow diagram is found which indicates into which type any particular type may evolve and the necessary form of the discontinuity causing that change. During the development, several additional results are reached. Clarification of the distinction between gravitational waves and a space-time’s Petrov type is found. The study of discontinuous hypersurfaces is found essentially equivalent to Trautman’s information approach to waves, and seems to give better motivation for its results. The Weyl technique is understood to be an important method for separation of coordinate and physical behaviors.