Geodesic
The metric which allows the pure radiation field
Theoretical and applied mechanics, Tome 23 (1997) no. 1, p. 151 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

We investigate a diagonal Riemannian metric. The metric represented by four unknown functions, two of them depend on $x^1$ only and two depend on $x^4$ only. We compose the Einstein tensor. The functions composing the metric tensor are determined from tho condition that the form of Einstein tensor correspond to the energy-momentum tensor of the pure radiation field. This is the special case of the electromagnetic field for which the electric and magnetic three-vectors are equal and perpendicular. 
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     title = {The metric which allows the pure  radiation field},
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Dragi Radojević. The metric which allows the pure  radiation field. Theoretical and applied mechanics, Tome 23 (1997) no. 1, p. 151 . http://geodesic.mathdoc.fr/item/TAM_1997_23_1_a8/