M.Sc. / General Relativity, as defined by Einstein's equations, defines the geometry of the universe. In Numerical Relativity, Einstein's equations are solved with the aid of numerical methods and computers. This dissertation discusses the ADM formulation of Numerical Relativity via a Cauchy approach. (ADM refers to the initials of the discoverers of this method: Arnowitt, Deser and Misner.) When working within relativistic equations, a computer algebra code is very useful and such a code is described in this dissertation. In order to illustrate computational cost saving techniques, only spherically symmetric space-times are considered. Furthermore, we present and test a numerical code that implements the standard ADM approach in order to accurately evolve a single black hole space-time. Finally, we discuss the implementation of a maximal slicing gauge condition that refines the numerical code by giving it singularity avoidance properties.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:9425 |
| Date | 15 August 2012 |
| Creators | Wright, Warren Peter |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
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