Hodge Theory on Compact Two-Dimensional Spacetimes and the Uniqueness of gij with a Specified Rij

Ihrig, Edwin

Canadian journal of mathematics, Tome 39 (1987) no. 6, pp. 1459-1474

Résumé

The main question we wish to address in this paper is to what extent does the Ricci curvature of a spacetime determine the metric of that spacetime. Although it is relatively easy to see that the full Riemann curvature uniquely determines the metric for a generic choice of curvature tensors (see [4], [10], [11], [14] and [15], and the references contained therein), very little has been discovered about whether, if ever, Ric (or the stress energy tensor in Einstein's equations for that matter) determines g. Most exact solution techniques for Einstein's equations look only for solutions that have the same symmetries as Ric. It is not true in general that g must inherit the symmetries of Ric. It is not even clear that there is a Ric such that every g with this Ricci tensor is known.

Détail

DOI : 10.4153/CJM-1987-069-6

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