Evolution systems for non-linear perturbations of background geometries

Details Evolution systems for non-linear perturbations of background geometries Evolution systems for non-linear perturbations of background geometries

2001-07-13

arxiv.org/abs/gr-qc/0107051v2

Phys.Rev. D65 (2002) 044008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, 3 figures, Revtex v3.0. Revised version to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.65.044008

The formulation of the initial value problem for the Einstein equations is at the heart of obtaining interesting new solutions using numerical relativity and still very much under theoretical and applied scrutiny. We develop a specialised background geometry approach, for systems where there is non-trivial a priori knowledge about the spacetime under study. The background three-geometry and associated connection are used to express the ADM evolution equations in terms of physical non-linear deviations from that background. Expressing the equations in first order form leads naturally to a system closely linked to the Einstein-Christoffel system, introduced by Anderson and York, and sharing its hyperbolicity properties. We illustrate the drastic alteration of the source structure of the equations, and discuss why this is likely to be numerically advantageous.

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