A Search for an Interior Solution

in General Relativity Using Lie-Baecklund Symmetries

by

David Neilsen

Brigham Young University

Abstract

The Einstein field equations describing a stationary, axially symmetric, rigidly rotating, relativistic, perfect fluid are reduced with a similarity transformation to ordinary differential equations. A Lie-Baecklund 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.

For more, peruse these PostScript files:

Introduction
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Appendix A (Pages 68, 69 and 70 are unfortunately blank.)
Appendix B
Appendix C