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Linear perturbations of a Schwarzschild black hole

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)

Identiferoai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:uir.unisa.ac.za:10500/1667
Date17 February 2015
CreatorsKubeka, Amos Soweto
ContributorsLesame, W. M., Bishop, N. T.
Source SetsSouth African National ETD Portal
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Format1 online resource (xvii, 161 leaves)

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