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

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

2001-07-10

arxiv.org/abs/gr-qc/0107030v1

Class.Quant.Grav. 19 (2002) 429-456

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/19/3/302

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.

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