Algebraically independent nth derivatives of the Riemannian curvature spinor in a general spacetime

Details Algebraically independent nth derivatives of the Riemannian curvature spinor in a general spacetime Algebraically independent nth derivatives of the Riemannian curvature spinor in a general spacetime

Nov 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cqgra...3.1133m&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 3, Nov. 1, 1986, p. 1133-1141.

Computer Science

25

Einstein Equations, Riemann Manifold, Spinor Groups, Vacuum, Canonical Forms, Covariance, Maxwell Equation, Scalars

Scientific paper

Explicit sets of spinor nth derivatives of the Riemann curvature spinor for a general spacetime are specified for each n so that they contain the minimal number of components enabling all derivatives of order m to be expressed algebraically in terms of these sets for n less than or equal to m; this generalizes an earlier result by Penrose (1960). The minimal sets are defined recursively in a manner convenient for use in the procedures for resolving the 'equivalence problem' of the local isometry of two given spacetimes. The actual numbers of quantities to be calculated are given and the reductions in these arising in special cases such as vacuum and conformally flat spacetimes, and spacetimes with vanishing Bach tensor, are discussed, as is the embodiment of the results in the CLASSI implementation (using the computer algebra system SHEEP) of the procedure for the equivalence problem. Finally, the possible relevance of the results to analytic and numerical methods of solving the Einstein equations is considered.

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