An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes

Details An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes

2011-04-07

arxiv.org/abs/1104.1356v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

We will present a complete set of equations, in the form of an Einstein-Bianchi system, that describe the evolution of generic smooth lattices in spacetime. All 20 independent Riemann curvatures will be evolved in parallel with the leg-lengths of the lattice. We will show that the evolution equations for the curvatures forms a hyperbolic system and that the associated constraints are preserved. This work is a generalisation of our previous paper arXiv:1101.3171 on the Einstein-Bianchi system for the Schwarzschild spacetime to general 3+1 vacuum spacetimes.

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