SELF-DUAL MAXWELL FIELDS ON CURVED SPACE-TIMES

We present a manifestly conformally invariant formulation of Maxwell e quations on asymptotically flat space-times. It is shown how to constr uct regular self-dual and antiself-dual fields from suitable radiation data, and the general solution as a sum of fields with both types of duality. The basic variable in this formalism is a scalar field F defi ned as the phase of the parallel propagator (associated with the Maxwe ll potential) from interior points to future null infinity along null geodesics. Field equations equivalent to the source free Maxwell's equ ations are derived for F. A perturbative solution based on Huygens' pr inciple is proposed. Exact solutions are found for H-spaces. The use o f these results on gravitational lensing is discussed. (C) 1996 Americ an Institute of Physics.