We firstly numerically recalculate the Ricci tensor of non-stationary axisymmetric
space-times (originally calculated by Chandrasekhar) and we find some discrepancies
both in the linear and non-linear terms. However, these discrepancies do not affect
the results concerning linear perturbations of a Schwarzschild black hole. Secondly,
we use these Ricci tensors to derive the Zerilli and Regge-Wheeler equations and use
the Newman-Penrose formalism to derive the Bardeen-Press equation. We show the
relation between these equations because they describe the same linear perturbations
of a Schwarzschild black hole. Thirdly, we illustrate heuristically (when the angular
momentum (l) is 2) the relation between the linearized solution of the Einstein vacuum
equations obtained from the Bondi-Sachs metric and the Zerilli equation, because
they describe the same linear perturbations of a Schwarzschild black hole. Lastly, by
means of a coordinate transformation, we extend Chandrasekhar's results on linear
perturbations of a Schwarzschild black hole to the Bondi-Sachs framework. / Mathematical Sciences / M. Sc. (Applied Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/1667 |
| Date | 17 February 2015 |
| Creators | Kubeka, Amos Soweto |
| Contributors | Lesame, W. M., Bishop, N. T. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (xvii, 161 leaves) |
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