Geodesic
Nonstatic centrally symmetric vacuum solution in the relativistic theory of gravitation
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 2, pp. 272-285

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A nonstatic centrally symmetric solution of the relativistic theory of gravitation in vacuum is constructed in the class of nondiagonal metrics on the basis of the general spherical solution of the Hilbert–Einstein equations – the Petrov metric. This shows that in the relativistic theory of gravitation Birkhoff's theorem is not valid, i.e., a nonstatic spherically symmetric body can create a nonstatic external field. It is shown that in all coordinates of the Minkowski space there exists at least one nonstatic spherically symmetric solution of the relativistic theory of gravitation in vacuum. 
@article{TMF_1991_88_2_a6,
     author = {A. V. Genk},
     title = {Nonstatic centrally symmetric vacuum solution in the relativistic theory of gravitation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {272--285},
     publisher = {mathdoc},
     volume = {88},
     number = {2},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a6/}
}
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A. V. Genk. Nonstatic centrally symmetric vacuum solution in the relativistic theory of gravitation. Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 2, pp. 272-285. http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a6/