Newman  showed analogies between the Liénard–Wiechert field [2-7] and the Robinson-Trautman (RT) solutions [8-10] of the Einstein gravitational equations. Here we present one more analogy: The Maxwell field produced by a point charge in arbitrary motion has the same algebraic type as the RT metrics. This result is possible because the Weert superpotential [3, 6, 7, 11-16] permits to construct an “electromagnetic Weyl tensor” which admits the Petrov classification [8, 17-24] as in general relativity.
International Frontier Science Letters (Volume 2)
J. L. Lopez-Bonilla et al., "Petrov Classification of the Liénard–Wiechert Field", International Frontier Science Letters, Vol. 2, pp. 16-17, 2014