UBC Theses and Dissertations
Initial data for axially symmetric black holes with distorted apparent horizons Tonita, Aaryn
The production of axisymmetric initial data for distorted black holes at a moment of time symmetry is considered within the (3+1) context of general relativity. The initial data is made to contain a distorted marginally trapped surface ensuring that, modulo cosmic censorship, the spacetime will contain a black hole. The resulting equations on the complicated domain are solved using the piecewise linear finite element method which adapts to the curved surface of the marginally trapped surface. The initial data is then analyzed to calculate the mass of the space time as well as an upper bound on the fraction of the total energy available for radiation. The families of initial data considered contain no more than few percent of the total energy available for radiation even in cases of extreme distortion. It is shown that the mass of certain initial data slices depend to first order on the area of the marginally trapped surface and the gaussian curvature of prominent features.
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