Counting solutions of Einstein's equations

Details Counting solutions of Einstein's equations Counting solutions of Einstein's equations

Jul 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cqgra..13.1931s&link_type=abstract

Classical and Quantum Gravity, Volume 13, Issue 7, pp. 1931-1948 (1996).

Physics

2

Scientific paper

The `degree of generality' of a physical field can be defined as the number of free parameters required to specify the nth derivative of the field at a given point in spacetime. Here, the degree of generality of Riemannian metrics both in the absence and in the presence of field equations and symmetries is investigated. The results are obtained in a number of different ways, using different basic field variables: for example, the components of the metric tensor, the connection, or the curvature tensor. This leads to a clear understanding of the relationships between the various sets of equations and provides guidance for tackling, for example, the problem of equivalence between Riemannian spaces.

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