Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

Abstract

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.

47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprints

References in corpus (2)

• A cure for unstable numerical evolutions of single black holes: adjusting the standard ADM equations
• Constraint propagation in the family of ADM systems

Cited by in corpus (8)

• Riemann Normal Coordinate expansions using Cadabra
• Maximal Slicing for Puncture Evolutions of Schwarzschild and Reissner-Nordström Black Holes
• An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime
• A Smooth Lattice construction of the Oppenheimer-Snyder spacetime
• An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes
• Deriving the ADM 3+1 evolution equations from the second variation of arc length
• Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole
• Summary of GR18 Numerical Relativity parallel sessions (B1/B2 and B2), Sydney, 8-13 July 2007