All Questions
66
questions with no upvoted or accepted answers
6
votes
1
answer
322
views
Pseudo-Riemannian 2D manifold (visualize time curvature)
My goal is to visualize somehow the curvature of time, as opposed to the curvature of space. I know that we generally talk about spacetime curvature altogether; however, the fact that spacetime has ...
- 719
4
votes
1
answer
402
views
What is the geometry of light cones if space is curved/non-Euclidean?
In light cone diagrams, the plane corresponding to the present is always the Euclidean one, but what if space is curved? Now, I've also seen diagrams where spacetime is supposed to be regarded as ...
- 241
3
votes
0
answers
84
views
Why are departures from flat spacetime geometry small on scales smaller than the Hubble radius?
In Chapter 5 of Baumann's cosmology book where he discusses structure formation starting from Newtonian perturbation theory, Baumann mentions at the beginning that
Newtonian gravity is a good ...
- 394
3
votes
0
answers
590
views
If gravity is due to curvature, how does gravity work in situations with no curvature?
The strength of the gravitational field falls off as the inverse square of the distance from a spherical source. It only falls off as the inverse of the distance from an extended cylindrical or line ...
- 394
3
votes
0
answers
392
views
What Would Negative Mass Do To Spacetime?
It's known that positive mass bends space-time to create a curvature. But if something had negative mass what would it do? Make it flat or like a crest?
- 527
3
votes
0
answers
217
views
Curvature and spacetime
Suppose that it is given that the Riemann curvature tensor in a special kind of spacetime of dimension $d\geq2$ can be written as $$R_{abcd}=k(x^a)(g_{ac}g_{bd}-g_{ad}g_{bc})$$ where $x^a$ is a ...
- 43
3
votes
2
answers
129
views
Does deformation of spacetime imply deformation of space?
In general relativity it is said that gravity is a deformation of spacetime. Does this deformation take place only when I consider space and time as one entity, or is this a real deformation in space ...
- 215
2
votes
1
answer
68
views
Understanding Wormholes Geometrically
Is the folding sheet analogy really that good for understanding what a wormhole is? After all, space-time curvature doesn't require any ambient space (it's intrinsic), as such a picture would suggest. ...
- 323
2
votes
0
answers
113
views
Riemann curvature tensor in real universe
The way Riemann Curvature tensors are usually introduced is as follows:
Take a vector v at point A, parallel transport it to B then to C then again back to A, the resulting vector v' will not point in ...
- 1,161
2
votes
0
answers
56
views
A geometric understanding of Kaluza-Klein theory?
Here's how I understand the Einstein field equations: in the presence of pure mass (no pressure), the eigen-basis of the Ricci tensor is the same as the particle's rest frame, and all 4 components are ...
- 2,475
2
votes
0
answers
84
views
Through what exact mechanism is the stress energy tensor bending spacetime?
In the Einstein field equations the metric related quantities are on one side, and the stress-energy tensor on the other.
What is the deeper mechanism of how nature actually implements this ...
- 101
2
votes
1
answer
120
views
(3+1)D solution to (2+1)D einstein equations?
Imagine a grid in 3D made of pipes smoothed so that it forms one continuous infinite surface. The surface is 2D but it fills 3D space.
Like this (at one instant):
Could any surface like this be a ...
user84158
2
votes
0
answers
20
views
About tests on the importance of general relativistic effects
I am dealing with the trajectories of charged particles in the vicinity of a Kerr black hole which is inmerse in an asymptotically uniform magnetic field. I pretend to make an estimation of the ...
- 21
2
votes
0
answers
62
views
About General Relativity and Reference Frames
So, I came up with this question which is intriguing me since a bit. Maybe it's stupid, but it's always better to ask.
The question is about inertial reference frames (I'll name them IRF)
We know ...
- 3,705
2
votes
0
answers
233
views
Examples of manifolds (not) being: flat, homogeneous and isotropic
I am looking for (at least) one example of the following manifolds:
Flat, homogeneous and isotropic
Curved, homogeneous and isotropic
Flat, non-homogeneous and isotropic
Flat, homogeneous and non-...
user17116