At. Barnaveli et My. Gogberashvili, ASYMPTOTICALLY NON-MINKOWSKIAN BUBBLES WITH GRAVITATIONAL REPULSION, Theoretical and mathematical physics, 113(2), 1997, pp. 1491-1496
It is usually assumed that spherical domain walls can be described by
the same equation of state as planar domains. In this case, the spheri
cal domain walls should also demonstrate gravitational repulsion, whic
h would contradict the Birkhoff theorem. However, this theorem does no
t apply to solutions that are not described by Minkowskian geometry at
infinity. In the thin-wall formalism, we consider the solution of the
Einstein equations that describes a spherical domain wall with gravit
ational repulsion and which is ''asymptotically non-Minkowskian.''