Robinson-Trautman solutions to Einstein's equations

Solutions to Einstein's equations in the form of a Robinson-Trautman metric are presented. In particular, we derive a pure radiation solution which is non-stationary and involves amassm, The resulting spacetime is of Petrov Type IIA special selection of parametric values throws up the feature of the particle 'rocket', a Type D metric. A suitable transformation of the complex coordinates allows the metrics to be expressed in real form. A modification, by setting m to zero, of the Type II metric thereby converting it to Type III, is then shown to admit a null Einstein-Maxwell electromagnetic field.