Geodesic
Spherically symmetric perturbations in a spatially flat universe
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 3, pp. 109-115 
R. K. Mukharlyamov; A. A. Popov. Spherically symmetric perturbations in a spatially flat universe. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 148 (2006) no. 3, pp. 109-115. http://geodesic.mathdoc.fr/item/UZKU_2006_148_3_a8/
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     author = {R. K. Mukharlyamov and A. A. Popov},
     title = {Spherically symmetric perturbations in a~spatially flat universe},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {109--115},
     year = {2006},
     volume = {148},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2006_148_3_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

A solution of the linearized Einstein's equations for a spherically symmetric perturbation of the ultrarelativistic fluid in the homogeneous and isotropic universe is obtained. Conditions on the boundary of the perturbation are discussed. The examples of particle-like and wave-like solutions are given.

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