Geodesic
Gravitational field of radiating non-twisting charged systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 35 (1978) no. 3, pp. 296-311 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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