Geodesic
Nonstatic centrally symmetric vacuum solution in the relativistic theory of gravitation
Teoretičeskaâ i matematičeskaâ fizika, Tome 88 (1991) no. 2, pp. 272-285 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {1991},
     volume = {88},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a6/}
}
TY  - JOUR
AU  - A. V. Genk
TI  - Nonstatic centrally symmetric vacuum solution in the relativistic theory of gravitation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1991
SP  - 272
EP  - 285
VL  - 88
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a6/
LA  - ru
ID  - TMF_1991_88_2_a6
ER  - 
%0 Journal Article
%A A. V. Genk
%T Nonstatic centrally symmetric vacuum solution in the relativistic theory of gravitation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1991
%P 272-285
%V 88
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1991_88_2_a6/
%G ru
%F TMF_1991_88_2_a6
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/

[1] Birkhoff G. D., Relativity and Modern Physiks, Harvard Univ. Press, Cambridge, 1923, P. 256 | Zbl

[2] Petrov A. Z., ZhETF, 44:5 (1963), 1525–1533 ; Уч. зап. Казанск. гос. ун-та, 123, No 2, 1963, 61–69; No 12, 21–29 | MR | Zbl

[3] Petrov A. Z., Novye metody v OTO, Nauka, M., 1966 | MR

[4] Smirnov V. I., Kurs vysshei matematiki, T. 3, Ch. 2, Nauka, M., 1974 | MR

[5] Bergmann P. G., Cahen M., Komar A. B., J. Math. Phys., 6 (1965), 1 ; Hamoui A., Ann. Inst. H. Poincare, A10 (1969), 195 | DOI | MR | Zbl

[6] Logunov A. A., Mestvirishvili M. A., TMF, 61 (1984), 327–346 ; ЭЧАЯ, 17:1 (1986), 5–160 ; Основы релятивистской теории гравитации, МГУ, М., 1986 | MR | Zbl | MR

[7] Genk A. V., Relyativistskaya teoriya gravitatsii s lineinym uravneniem svyazi, Dep. VINITI, No 5982-V87; Материалы 7-й Всесоюзной гравитационной конференции, Изд-во ЕГУ, Ереван, 1988, 186–187

[8] Vlasov A. A., Logunov A. A., TMF, 64:1 (1985), 3–6 | MR | Zbl

[9] Genk A. V., TMF, 79:3 (1989), 473–480 ; Материалы 7-й Всесоюзной гравитационной конференции, Изд-во ЕГУ, Ереван, 1988, 188–189 | MR

[10] Fok V. A., Teoriya prostranstva, vremeni i tyagoteniya, GITTL, M., 1955

[11] Vyblyi Yu. P., Materialy 7-i Vsesoyuznoi gravitatsionnoi konferentsii, EGU, Erevan, 1988, 171–172

[12] Unt V. A., Izvestiya vuzov. Fizika, 1961, no. 4, 3–8; Асанов Р. А., Препринт No Р2 86-525, ОИЯИ, Дубна, 1986 | MR

[13] Avakyan R. M., Tochnye resheniya uravnenii Einshteina i ikh fizicheskaya interpretatsiya, Izd-vo Tartusskogo un-ta, Tartu, 1988, 22–23