Mathematics – Logic
Scientific paper
Jul 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004phdt........12m&link_type=abstract
Thesis (PhD). BRIGHAM YOUNG UNIVERSITY, Source DAI-B 65/01, p. 255, Jul 2004, 119 pages.
Mathematics
Logic
Scientific paper
This dissertation is a description of a variety of methods of solving the Einstein equations describing the gravitational interaction in different mathematical and astrophysical settings. We begin by discussing a numerical study of the Einstein-Yang-Mills-Higgs system in spherical symmetry. The equations are presented along with boundary and initial conditions. An explanation of the numerical scheme is then given. This is followed by a discussion of the solutions obtained together with an interpretation in the context of gravitational collapse and critical phenomena at the threshold of black hole formation. Following this, we generalize the same system to axisymmetry. The full, gravitational equations are presented along with a short discussion of the problems we encountered in trying to solve these. As a first step we consider evolving the matter fields in flat space. The simplified equations are given and the numerical scheme implemented to solve them discussed. We then consider some analytic techniques to understanding the Einstein equations and the gravitating systems they should describe. One such is to change the spacetime dimension. This we do in considering magnetic solutions to the (2 + 1) Einstein-Maxwell-Dilaton system with nonzero cosmological constant. The solutions are investigated to determine whether these correspond to “soliton”-like solutions or black holes. As another example of this general approach, we introduce an extra timelike coordinate into the spherically symmetric vacuum system, and attempt to find a solution comparing the result to the more well known Schwarzschild solution. Finally, we give a short description of some preliminary work which will combine some of these numerical and analytical techniques. This approach simply takes the matter fields as weak and propagates them on a fixed spacetime background. In our particular case, we intend to study the evolution of Maxwell fields in the Schwarzschild geometry. We provide motivation for this as well as present the equations describing the system.
No associations
LandOfFree
Finding solutions to the Einstein equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Finding solutions to the Einstein equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finding solutions to the Einstein equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-771665