A rotating pure radiation field

Abstract

Starting with the Kerr solution, we generate an algebraically special pure radiation solution of Einstein's field equations. This solution is axisymmetric, asymptotically flat and regular on the axis. The metric is determined up to a linear second-order ordinary differential equation for which only particular solutions are known. The transformation to Bondi--Sachs coordinates is determined as a power series expansion in terms of the inverse radial coordinate. The relation between our derivation and another approach using Cauchy--Riemann structures is established and the underlying Cauchy--Riemann structure of our solution is given.