Geodesic
Antigraviting bubbles with non-Minkowskian asymptotic
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 346-352

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Usually it is assumed that the spherical domain walls are described by the same state equation as the flat ones. In this case they also must be gravitationally repulsive, what is seemingly in contradiction with Birkhoff's theorem. However, this theorem is not applicable to solutions which do not display Minkowski geometry at infinity. In the paper a solution of Einstein equations describing the stable gravitationally repulsive spherical domain wall is considered in thin wall formalism for the case of non-Minkowskian asymptotic. 
@article{TMF_1997_113_2_a10,
     author = {A. Barnaveli and M. Gogberashvili},
     title = {Antigraviting bubbles with {non-Minkowskian} asymptotic},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {346--352},
     publisher = {mathdoc},
     volume = {113},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a10/}
}
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A. Barnaveli; M. Gogberashvili. Antigraviting bubbles with non-Minkowskian asymptotic. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 2, pp. 346-352. http://geodesic.mathdoc.fr/item/TMF_1997_113_2_a10/