Abstract
The non-local part of the gravitational field Cabcd can be generated by the 16-component Lanczos tensor potential Labc. When six gauge conditions are imposed, Labe;e=0, its ten degrees of freedom match those of the Weyl tensor. The Penrose wave equation for Cabcd can be independently derived from that for Labc. The consistency between Labc and Cabcd is also shown by the compatibility of their algebraic classifications. An unexpected insight into the relationship of Labc and Cabcd is found in "Euclidean gravity" which in turn leads to the introduction of a gravitational Green's tensor [Formula: see text] corresponding to the potential Labc.
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