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

摘要

We will present results of a numerical integration of a maximally slicedSchwarzschild black hole using a smooth lattice method. The results show nosigns of any instability forming during the evolutions to t=1000m. Theprinciple features of our method are i) the use of a lattice to record thegeometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADMequations to the lattice and iii) the use of the Bianchi identities to assistin the computation of the curvatures. No other special techniques are used. Theevolution is unconstrained and the ADM equations are used in their standardform.