Algorithms for computer algebra calculations in spacetime I. The calculation of curvature

Details Algorithms for computer algebra calculations in spacetime I. The calculation of curvature Algorithms for computer algebra calculations in spacetime I. The calculation of curvature

1996-01-22

arxiv.org/abs/gr-qc/9601036v1

Class.Quant.Grav. 13 (1996) 2289-2310

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, latex2e (requires amstex.sty, mapleenv.sty). See also http://astro.queensu.ca/~grtensor/papers/pmsl96/pmsl96.html

Scientific paper

10.1088/0264-9381/13/8/021

We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of spacetimes, and distinct coordinates and tetrads for a given spacetime. Within the system GRTensorII, we find that there is no single preferred approach on the basis of speed. Rather, we find that the fastest algorithm is the one that minimizes the amount of time spent on simplification. This means that arguments concerning the theoretical superiority of an algorithm need not translate into superior performance when applied to a specific spacetime calculation. In all cases it is the global simplification strategy which is of paramount importance. An appropriate simplification strategy can change an untractable problem into one which can be solved essentially instantaneously.

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