Axisymmetric Numerical Relativity

Abstract

This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially) constrained scheme with elliptic gauge conditions arising from maximal slicing and conformal flatness. The second is a strongly hyperbolic first-order formulation obtained by combining the (2+1)+1 formalism with the Z4 formalism. A careful study of the behaviour of regular axisymmetric tensor fields enables us to cast the equations in a form that is well-behaved on the axis. Further topics include (non)uniqueness of solutions to the elliptic equations arising in constrained schemes, and comparisons between various boundary conditions used in numerical relativity. The numerical implementation is applied to adaptive evolutions of nonlinear Brill waves, including twist.

PhD thesis, University of Cambridge, September 2005. LaTeX, 310 pages, 34 figures, 5 tables. Some typos fixed

References in corpus (8)

• The Dynamics of General Relativity
• Evolution of Binary Black Hole Spacetimes
• Numerical Relativity Using a Generalized Harmonic Decomposition
• Boundary Conditions for the Einstein Evolution System
• Optimal Constraint Projection for Hyperbolic Evolution Systems
• Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
• A strongly hyperbolic and regular reduction of Einstein's equations for axisymmetric spacetimes
• A model problem for the initial-boundary value formulation of Einstein's field equations

Cited by in corpus (7)

• Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• A Pseudospectral Method for Gravitational Wave Collapse
• Self force via $m$-mode regularization and 2+1D evolution: II. Scalar-field implementation on Kerr spacetime
• Evolutions of centered Brill waves with a pseudospectral method
• A minimization problem for the lapse and the initial-boundary value problem for Einstein's field equations
• On the linear stability of the extreme Kerr black hole under axially symmetric perturbations