All Questions
17
questions
2
votes
1
answer
124
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
2
votes
1
answer
100
views
Reducing Tensor-rank by fixing an argument
Assume for example that you are given a (2,0) tensor $T^{\mu\nu}$ and you want to create
a vector, i.e., a (1,0) tensor out of it. Is it possible to just fix an index of
$T^{\mu\nu}$ while keeping the ...
- 56
2
votes
1
answer
3k
views
Ricci scalar curvature in FLRW flat universe
I have a simple question about the relation between the Ricci scalar curvature and the $k$ constant in the Friedmann–Lemaître–Robertson–Walker solution. Assuming $k=0$, such that the space can be ...
- 308
1
vote
0
answers
98
views
Where is the warped throat in Klebanov-Strassler geometry?
In string theory, it is common to work in the Klebanov-Strassler geometry to find AdS and dS vacua. Applications are that anti-branes can be placed at the tip of this deformed/warped conifold to ...
- 119
2
votes
2
answers
288
views
Topology in cosmology
Usually in cosmology, we make the hypothesis that the universe is isotropic.
Which conditions does this hypothesis impose on the topology of the universe? Does it fix completely the topology? Are all ...
- 1,335
1
vote
1
answer
61
views
Ambiguity in measuring the speeds of galaxies
People measure the speeds of galaxies via the redshift effect. However, considering our spacetime as a non-flat manifold implies that measuring the speeds of any two objects not in the same tangent ...
1
vote
1
answer
100
views
Explaining accelerating spacetime expansion?
I should begin by noting that I am NOT a physicist, I study differential geometry and so my physics background is extremely limited. That being said I was reading a textbook on general relativity and ...
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
2
votes
2
answers
466
views
Why isn't general relativity equivalent to Newtonian gravity?
I know this question may seem a bit laughable, but the way the equations for general relativity are formed is through Poisons equation:
$$\nabla^2\phi=4 \pi G \rho$$
Which are formed using Newton's ...
- 775
10
votes
3
answers
3k
views
What are the pros and cons of Einstein-Cartan Theory?
As an alternative to General Relativity, I hear that it can avoid the initial big bang singularity as well as the singularities in black holes, so why does it appear to be talked about so little? If ...
- 2,123
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
2
votes
0
answers
143
views
Which specific smooth structure are we using in general relativity?
In this lecture by Fredric Schuller it is said that in the case of a non compact four dimensional manifold there is a non countable infinity of differentiable or smooth manifolds that are NOT ...
user56963
0
votes
1
answer
243
views
General relativity with space and time on different footing
Excerpt from the textbook below. It seems ambiguous what the author means and I am unable to proceed.
Imagine that you live in a Universe where Einstein never existed. Instead, he was replaced by ...
- 323
5
votes
0
answers
782
views
Does any spacetime admit a global foliation in spacelike hypersurfaces?
In the comments of this question the following new questions came up: in general relativity, local coordinates can be found around any point, that single out a time coordinate and a three dimensional ...
- 9,304