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

Abstract

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.

References in corpus (4)

• Riemann Normal Coordinate expansions using Cadabra
• An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime
• A Smooth Lattice construction of the Oppenheimer-Snyder spacetime
• Deriving the ADM 3+1 evolution equations from the second variation of arc length

Cited by in corpus (3)

• A numerical study of the Regge Calculus and Smooth Lattice methods on a Kasner cosmology
• Evolutions of Gowdy, Brill and Teukolsky initial data on a smooth lattice
• Two dimensional axisymmetric smooth lattice Ricci flow