All Questions
13
questions
-1
votes
1
answer
53
views
If an area in 2D cannot be curved and finite is the same regarding the space of our pressumed 3D universe?
Is the sentence in the title right that our universe is infinite? And if so does it mean that stars are not evenly distributed along our universe but they all move from a populated centre to a fairly ...
- 2,255
2
votes
1
answer
123
views
Could the universe have a form of a $T^3$-torus?
Cosmological measurements suggest that we live in a flat universe. However, what might be less clear is its topology. So could the flat universe have the form of a $T^3$-torus, i.e. the torus whose ...
- 9,778
0
votes
0
answers
41
views
In general relativity, could our curved spacetime be embedded in a higher dimension flat spacetime (5D+1) of the compatible metric? [duplicate]
I took General Relativity at university, years ago and have a question that has recently occurred to me. This might be a dumb one, so I apologise if the answer is a well known negative.
Mathematically,...
- 1,087
0
votes
2
answers
77
views
Is there any way to prove that contrarly to a flat 3D space, a curved 3D space can only be constructed in a 4D manifold?
This question is a result of me trying to understand how this universe can be possibly infinite if it isn't infinitely old. So to compare with an area that is flat it can be constructed both in 2D and ...
- 2,255
0
votes
1
answer
105
views
What does a universe with a boundary look like?
Physically, what would it look like if we lived in a universe with a boundary at finite distance?
- 423
1
vote
1
answer
175
views
Self-intersecting universe
General relativity says space-time is a $4$-dimensional manifold which may have non-zero global curvature. Now if we take a random curve or surface or $n$-fold, it may fail to be a manifold because it ...
- 111
-1
votes
2
answers
1k
views
Does the expansion of the Universe into a higher dimensional space imply that 4D objects are real?
It is my understanding that objects in the Universe are not just getting farther apart but space itself is expanding and so in some real sense, higher-dimensional geometry is "real" -- if so, on a ...
- 189
1
vote
2
answers
142
views
Allowable spacetime deformations [closed]
What deformations are possible with spacetime?
By 'deformation' I am referring to the kind of change in spacetime caused by the presence of a mass which deforms spacetime sufficiently to deflect ...
- 29
0
votes
3
answers
1k
views
Is the universe 5 dimensional space-time or 4?
we've been told that in General Relativity (GR), matter tells space how to curve and space tells matter how to move. But my question is, if 3 dimensional space was curved by matter then it should be ...
- 53
1
vote
0
answers
220
views
Can universe be a closed manifold?
I had a question at MSE which gave a rise to another question.
Maxwell equations can be written in form $$d\star F = J$$
Then by Stokes theorem we have
$$ \int_U J = \int_U d \star F = \int_{\...
- 748
1
vote
0
answers
776
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-...
- 111
20
votes
2
answers
3k
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 ...
- 847
125
votes
6
answers
11k
views
What is known about the topological structure of spacetime?
General relativity says that spacetime is a Lorentzian 4-manifold $M$ whose metric satisfies Einstein's field equations. I have two questions:
What topological restrictions do Einstein's equations ...
- 1,734