Asymptotically null slices in numerical relativity

Hilditch, David Matthew (2007) Asymptotically null slices in numerical relativity. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The work in this thesis concerns numerical evolution of the equations of General Relativity. The motivation is towards astrophysics through the choice of coordinates adapted to outgoing gravitational waves far from the strong-field region of a given spacetime. These asymptotically null coordinates allow a large region of spacetime to be evolved at a negligible computational cost.

The behaviour of various gauge conditions (coordinate choices) can be studied without the resorting to the Einstein equations, but instead evolving coordinates on a known background. This “pure-gauge” approach is used to find gauge conditions suitable for evolving asymptotically null initial data.

Breakthroughs in numerical relativity have relied on a constraint damping technique. In the work that follows constraint damping is used to evolve asymptotically null initial data with various formulations of the Einstein equations.

Characteristic analysis of a given formulation allows for the construction of maximally dissipative and constraint preserving boundary conditions; such conditions are implemented and studied numerically on both flat and asymptotically null slices.

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