Trishin

Null solutions of the source-free Maxwell equations in the Minkowski space-time are considered. It is well known that a principal null direction of the null electromagnetic field defines a shear-free geodesic null congruence. Conversely, null Maxwell fields can be obtained from the (analytic) shear-free congruence via the Robinson theorem. We present the explicit formula for the electromagnetic field derived from the Robinson and Kerr theorems. The solution depends on two analytic functions of two and three complex variables.