CURVATURE-FREE ASYMMETRIC METRIC CONNECTIONS AND LANCZOS POTENTIALS IN KERR-SCHILD SPACETIMES

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.