Third-order tensor potentials for the Riemann and Weyl tensors. II: Singular solutions

Details Third-order tensor potentials for the Riemann and Weyl tensors. II: Singular solutions Third-order tensor potentials for the Riemann and Weyl tensors. II: Singular solutions

May 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984gregr..16..423b&link_type=abstract

General Relativity and Gravitation, Volume 16, Issue 5, pp.423-433

Statistics

Applications

8

Scientific paper

The analysis of the admissibility of a potential representation for the Riemann tensor is here continued. As in the preceding paper, the starting point is to regard the relationship between the Riemann tensor and its possible potential as a system of partial differential equations determining the unknown potential. The first result, strengthening a previous conclusion, is that there never exist ordinary solutions. Surprisingly enough, in a four-dimensional Riemannian manifold the existence of singular solutions is established without requiring any integrability condition. Possible applications and generalizations are also suggested.

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