F. Andersson et Sb. Edgar, CURVATURE-FREE ASYMMETRIC METRIC CONNECTIONS AND LANCZOS POTENTIALS IN KERR-SCHILD SPACETIMES, Journal of mathematical physics, 39(5), 1998, pp. 2859-2861
The set of spinor equations linking the curvature spinors of a Riemann
-Cartan space with the curvature spinors of the corresponding Riemann
space is derived, and these are used to establish a simple relationshi
p between Psi-flat connections of the Riemann-Cartan space and Lanczos
potentials of the Riemann space. This not only yields, very easily, a
recent result of Bergqvist for the Kerr metric, but also enables Berg
qvist's result to be generalized; specifically we show that a curvatur
e-free connection, associated with a class of Kerr-Schild metrics, can
be identified as a Lanczos potential for the Weyl conformal curvature
spinor of these spaces. (C) 1998 American Institute of Physics.