An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime

Details An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime

2011-01-17

arxiv.org/abs/1101.3171v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

minor changes to conform with companion paper, new appendix

Scientific paper

The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacetime. This is the first of two papers. In the following paper we will extend the ideas developed here to general vacuum spacetimes. In this paper we will demonstrate our ideas on a Schwarzschild spacetime and give detailed numerical results. For suitable choices of lapse function we find that the system gives excellent results with long term stability.

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