# A Search for an Interior Solution

in General Relativity
Using Lie-Baecklund Symmetries

by
## David Neilsen

at
### 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.

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