Abstract
Using the Gauss-Codazzi equations, the behavior of a singular hypersurface, which divides the universe into two Friedmann-Robertson-Walker space-time regionsV + andV −, 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 inV ± 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 ofV ± or both are Schwarzschild-de Sitter space-time too.
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Maeda, K. Bubble dynamics in the expanding universe. Gen Relat Gravit 18, 931–951 (1986). https://doi.org/10.1007/BF00773558
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DOI: https://doi.org/10.1007/BF00773558