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Linear perturbations of a Schwarzschild black holeKubeka, Amos Soweto 17 February 2015 (has links)
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)
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Linear perturbations of a Schwarzschild black holeKubeka, Amos Soweto 17 February 2015 (has links)
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)
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