I What Would the Universe Look Like as a Manifold with Boundary?

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what would the universe look like if its a manifold with boundary? what would it look like at the boundary? and what happens if u try to touch the boundary? is it just a black wall that's unbreakable?
 
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This would depend on what kind of boundary conditions you impose. As far as we can tell though, there is no evidence whatsoever to imply a boundary.
 
DDTG Global said:
what would the universe look like if its a manifold with boundary? what would it look like at the boundary? and what happens if u try to touch the boundary? is it just a black wall that's unbreakable?
There's no working model of the universe with a boundary.
 
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From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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