Einstein's Equations with Asymptotically Stable Constraint Propagation

Details Einstein's Equations with Asymptotically Stable Constraint Propagation Einstein's Equations with Asymptotically Stable Constraint Propagation

1998-09-04

arxiv.org/abs/gr-qc/9809023v2

J.Math.Phys. 40 (1999) 909-923

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, submitted to JMP, added reference for section 2

Scientific paper

10.1063/1.532694

We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The extended system of equations reproduces the usual dynamics on the constraint surface of general relativity, and therefore naturally includes the solutions to Einstein gravity. The main feature of this extended system is that, at least for a linearized version of it, the constraint surface is an attractor of the time evolution. This feature suggests that this system may be a useful alternative to Einstein's equations when obtaining numerical solutions to full, non-linear gravity.

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