Abstract
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 a mass m, The resulting spacetime is of Petrov Type II A 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.
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Davidson, W. Robinson–Trautman solutions to Einstein’s equations. Gen Relativ Gravit 49, 22 (2017). https://doi.org/10.1007/s10714-017-2195-x
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DOI: https://doi.org/10.1007/s10714-017-2195-x