Date of Graduation
Eberly College of Arts and Sciences
Physics and Astronomy
An analysis of all known spherically symmetric solutions to the field equations originating from the Riemann tensor quadratic curvature Lagrangian is presented. A new exact solution is found for the field equation originating from the "energy-momentum" equation of the gauge gravity theory. Imposing equivalence between the Palatini and standard variational field equations yields an algebraic condition that restricts the number spacetime solutions to gauge gravity. A class of spherically symmetric solutions to the conformally invariant theory of gravitation is shown to be shared by the gauge gravity field equations. An analysis of a spherically symmetric solution to the conformal gravity field equations is also presented.;Point particle orbital dynamics in both the Schwarzschild and Reissner-Nordstrom black hole spacetimes are analyzed as 2-d conservative bifurcation phenomena. The classification is based on a study of coalescing fixed points and the parameter values at which these bifurcations occur. Physically distinct behaviors are separated by bifurcation points while dynamically distinct cases are divided into various regions of the phase-plane by the separatrix. The Schwarzschild dynamics exhibit both saddle-center and transcritical bifurcation points and a calculation of periastron precession is presented that incorporates a phase-plane analysis of the relativistic equations of motion. Level curves of constant energy are illustrated for both timelike and null geodesics and a phase-plane analysis of dynamical invariance between the proper and coordinate time reference frames is discussed. The Reissner-Nordstrom dynamics exhibit saddle-center, transcritical, pseudo-transcritical, and additional bifurcations that combine all three previous bifurcations in various combinations. Periastron precession in the Reissner-Nordstrom spacetime is analyzed using the phase-plane and bifurcation techniques and extended to include a bifurcation point of the dynamics. A numerical solution at these parameter values illustrates that such orbits typically yield a much larger precession value compared to the standard value for timelike, precession. The "acausal" geodesics considered by Brigman are also discussed and their precession value is calculated.
Dean, Bruce Herold, "Variational results and solutions in gauge gravity and a bifurcation analysis of black hole orbital dynamics" (1999). Graduate Theses, Dissertations, and Problem Reports. 3163.