Projective differential geometry and geodesic conservation laws in general relativity, II: Conservation laws.

Details Projective differential geometry and geodesic conservation laws in general relativity, II: Conservation laws. Projective differential geometry and geodesic conservation laws in general relativity, II: Conservation laws.

Nov 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984gregr..16.1063p&link_type=abstract

General Relativity and Gravitation, Volume 16, Issue 11, pp.1063-1075

Physics

7

General Relativity

Scientific paper

We examine the geodesic conservation laws associated with the projective actions discussed in our earlier paper with the same overall title. Using the Cartan formalism, a one-to-one correspondence between a class of these actions and all geodesic conservation laws is possible. In particular there is a natural geometric interpretation of Killing tensors. Homothetic motions are shown to correspond to conserved quantities on all geodesies (not just null ones). The same approach identifies homothetic Killing tensors and a universal quadratic first integral which reduces to the conformai Killing tensor case on null geodesics.

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