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Journals and Conferences
It will be shown that the truncation error for the Regge Calculus, as an approximation to Einstein’s equations, varies as O(∆) where ∆ is the typical discretization scale. This result applies to any metric, whether or not it is a solution of the vacuum Einstein equations. It is in this sense that the Regge Calculus is not a discrete representation of… (More)
A new lattice based scheme for numerical relativity will be presented. The scheme uses the same data as would be used in the Regge calculus (eg. a set of leg lengths on a simplicial lattice) but it differs significantly in the way that the field equations are computed. In the new method the standard Einstein field equations are applied directly to the… (More)
A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve three basic steps. First, the coordinate quantities such as the Riemann and extrinsic curvatures are extracted from the… (More)
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… (More)
Cadabra is a powerful computer program for the manipulation of tensor equations. It was designed for use in high energy physics but its rich structure and ease of use lends itself well to the routine computations required in General Relativity. Here we will present a series of simple examples showing how Cadabra may be used, including verifying that the… (More)
We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the… (More)
We will show that the ADM 3+1 evolution equations, for a zero shift vector, arise naturally from the equations for the second variation of arc-length.
We present test results for the smooth lattice method using an OppenheimerSnyder spacetime. The results are in excellent agreement with theory and numerical results from other authors.
A detailed analysis of the Riemann tensor in the neighbourhood of one bone and of the extrinsic curvature in the neighbourhood of one triangular face in a simplicial geometry is presented. Unlike most previous analyses this analysis makes no reference to any particular choice of smoothing scheme. Explicit formulae will be presented for both the Riemann and… (More)