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

Abstract

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.

minor changes to conform with companion paper, new appendix

References in corpus (3)

• Riemann Normal Coordinate expansions using Cadabra
• 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 (9)

• A numerical study of the Regge Calculus and Smooth Lattice methods on a Kasner cosmology
• An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes
• On the discrete version of the Schwarzschild problem
• On the discrete version of the black hole solution
• On the discrete version of the Kerr-Newman solution
• Evolutions of Gowdy, Brill and Teukolsky initial data on a smooth lattice
• On the discrete version of the Kerr geometry
• On the discrete version of the Reissner-Nordström solution
• Two dimensional axisymmetric smooth lattice Ricci flow