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Is it plausible for spacetime to be shaped something like a torus? [duplicate]

I have heard three theories for how space-time is shaped, flat, sphere-like, or saddle-like. Flat is the most likely, as all our measurements implies that space time has curvature close to 0. Is it ...
426 views

Our Universe Can't be Looped? [duplicate]

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
503 views

Do we expect that the universe is simply-connected? [duplicate]

I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe cannot be simply-connected, since the 3-...
101 views

How does GR determine the topology of spacetime? [duplicate]

The crux of GR is the action $$S=\int _\mathcal M d^n x \sqrt{|g|}\,R$$ Varying this and setting $\delta S=0$ gives you the Einstein field equations. However, that only determines the metric, not ...
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Does the Einstein field equation uniquely determines the topology of spacetime? [duplicate]

I am trying to understand whether the Einstein field equation uniquely determines the topology of spacetime. As far as I know, given a metric, we can always find the induced topology. However, I was ...
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Expansion of Universe: Spacetime metric and Topological Variations? [duplicate]

There are many posts, questions, comments and excellent answers on this website pertaining to cosmology, expansion, universe, spacetime et cetera. Yet, the following question was not asked or answered,...
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What is the shape of the universe? [duplicate]

If it's flat then how a volume can be flat? And I've read that it's actually not flat .....it's a "Poincaré dodecahedral space". Any suggestions for books posts or articles are highly appreciated.
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Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
3k views

Can spacetime be non-orientable?

This question asks what constraints there are on the global topology of spacetime from the Einstein equations. It seems to me the quotient of any global solution can in turn be a global solution. In ...
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Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, $g_{\mu\nu}$...
2k views

Is spacetime simply connected?

As I've stated in a prior question of mine, I am a mathematician with very little knowledge of Physics, and I ask here things I'm curious about/things that will help me learn. This falls into the ...
2k views

How do wormholes work?

Firstly, I understand that we have no observational evidence for 'wormholes'. They are theorised solutions to general relativity equations. That said, if macroscopic wormholes do exist---how do they ...
2k views

What manifold is spacetime?

In General Relativity, spacetime is a $4$-dimensional manifold with one Lorentzian metric tensor defined on it. In the Special Relativity case what manifold is spacetime is quite clear: it is ...