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Curvature collineations and the determination of the metric from the curvature in general relativity

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Abstract

It is shown that for a very general class of space-times, the componentsR a bcd of the curvature tensor determine the metric components up to a constant conformal factor. This general class contains most of those cases which are usually considered to be interesting from the point of view of Einstein's general relativity theory. The connection between the above result and the existence of proper curvature collineations is given.

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Authors and Affiliations

  1. Department of Mathematics, University of Aberdeen, Edward Wright Building, AB9 2TY, Aberdeen, Scotland, United Kingdom

    G. S. Hall

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  1. G. S. Hall
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Additional information

This essay received an honourable mention from the Gravity Research Foundation for the year 1982.

Presently on leave at the Department of Mathematics, Monash University Clayton, Victoria 3168, Australia.

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Hall, G.S. Curvature collineations and the determination of the metric from the curvature in general relativity. Gen Relat Gravit 15, 581–589 (1983). https://doi.org/10.1007/BF00759572

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