Abstract
In general relativity the non-local part of the gravitational field is described by the 10 degrees of freedom of the Weyl conformal curvature tensor
C
abcd
. In every space-time the Weyl field
C
abcd
is derivable from a potential
L
abc
which has at most 16 algebraically independent components reducing to 10 degrees of freedom when the six gauge conditions
L
ab
s
; s
= 0 are imposed. The potential
L
abc
discovered by Lanczos was shown by Illge to have an extremely simple vacuum wave equation, namely, □
L
abc
≡
g
sm
L
abc
;
s
;
m
= 0. Using tensor, spinor and spin-coefficient methods we give some solutions of this new vacuum wave equation in some spacetimes containing one or more preferred vector fields.
Cited by
24 articles.
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