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

TL;DR

This paper develops a new evolution system based on the second Bianchi identity for vacuum spherically symmetric spacetimes, demonstrating its stability and accuracy through numerical results on Schwarzschild spacetime.

Contribution

It introduces an Einstein-Bianchi system for smooth lattice general relativity applied to Schwarzschild spacetime, with potential extension to general vacuum spacetimes.

Findings

System achieves long-term stability in numerical simulations.

Excellent accuracy demonstrated on Schwarzschild spacetime.

Framework paves the way for broader applications in vacuum solutions.

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.