Using the Gauss-Codazzi equations, the behavior of a singular hypersurface, which divides the universe into two Friedmann-Robertson-Walker space-time regions V+ and V-, is investigated. The equation of motion for a spherical bubble in the expanding universe is presented and the physical meaning of the equation is clarified. The equations of state for fluids in V± and on the boundary shell, which should be determined by microscopic physics, are arbitrary in the present geometrical approach. The derived equations are quite similar to those for a shell in a vacuum and can be applied to the case that one of V± or both are Schwarzschild-de Sitter space-time too.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)