Geodesic
Gravitational field of radiating non-twisting charged systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 3, pp. 296-311

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The Newman–Penrose spin coefficient formalism is used to obtain in explicit form all solUtions of the Einstein–Maxwell equations with thermodynamic radiation (i.e., radiation of Isaacson type) under the conditions that: 1) the radiation propagates along a geodesic congruence determined by the principal isotropic direction of the Maxwell tensor; 2) this congruence is a non-twisting, shear-free diverging congruence; 3) the spacetime has no angular singuiarities or background (low-frequency) gravitational waves. 
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     author = {V. I. Kslebnikov},
     title = {Gravitational field of radiating non-twisting charged systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {296--311},
     publisher = {mathdoc},
     volume = {35},
     number = {3},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1978_35_3_a1/}
}
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V. I. Kslebnikov. Gravitational field of radiating non-twisting charged systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 3, pp. 296-311. http://geodesic.mathdoc.fr/item/TMF_1978_35_3_a1/