Physically, what would it look like if we lived in a universe with a boundary at finite distance?
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2$\begingroup$ 1- What do you mean by "universe with a boundary"? General relativity usually considers spacetime to be a manifold, i.e. have no boundary. 2. The edge of the observable universe already is a boundary at some sense at a finite distance. What is different about your setup? $\endgroup$– ACuriousMind ♦Commented Sep 18, 2020 at 15:22
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$\begingroup$ Quite literally, suppose assumption 1 was false, and our spacetime is a manifold with a boundary, what happens. $\endgroup$– YankyLCommented Sep 21, 2020 at 13:42
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$\begingroup$ The model of the Friedmann Universe assumes isotropy, i.e. there exists no preferred location in the Universe. This assumption would not be valid anymore in your model, since you don't expect the Universe to look the same near its boundary or e.g. at its center. Hence you could probably make an absolute map of your Universe (based on the geometry of your choice), and find your position inside by comparing local effects to large scale effects. $\endgroup$– PxxCommented Oct 26, 2020 at 21:11
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Probably the best answer would be that such a universe would have a physical boundary, and the dynamics would be based on the Schwartzchild metric.
https://en.wikipedia.org/wiki/Schwarzschild_metric
I would suggest an approximately spherically symmetric universe with a spherical shell boundary made of a suitable material (possibly fictional), the outside a vacuum, and the inside some matter and radiation of your choice. If the initial condition is a hot gas (but not so hot as to damage the shell), then it would have some attributes similar to a finite hyper-spherical universe in a process of collapse rather than expansion. The collapse would not be geometrical as in the universe we have. Rather it would just be a gravitational collapse which near the center might well seem somewhat like a Friedmann model collapse, but my guess is that there would not be any Hubble law effect. Ultimately, the matter and some of the radiation would become a single black hole.
