Abstract
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.