All Questions
Tagged with spacetime differential-geometry
347
questions
3
votes
1
answer
2k
views
What bends fabric of space-time?
I know that mass can bend fabric of space-time, which causes gravity by making an object curve around a planet or star but is there anything else that can bend it?
Other energy sources, forces ...
- 211
2
votes
1
answer
203
views
Symmetries of spacetime and objects over it
I guess according to mathematical didactic, we first think of spacetime as a set and we reason about elements of its topology and then it's furthermore equipped with a metric. Appearently it is this ...
- 8,523
7
votes
4
answers
1k
views
Hamiltonian and the space-time structure
I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian.
Space-time structure dictates the form of ...
- 2,619
2
votes
0
answers
2k
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de Sitter and anti de Sitter metric
Is the following correct for the distance $d$ from the origin $(0,0)$ to point $(t,x)$ in the 2-dimensional
de-Sitter and anti de-Sitter spaces? Here, $t$ is time and the distance may be called the ...
- 143
4
votes
2
answers
780
views
How should one interpret the de Sitter slicings?
When 'constructing' the usual de Sitter space in $\mathcal{M^5}$ by invoking the contraint $-X^{2}_{0} +X^{2}_{1} +X^{2}_{2} +X^{2}_{3} + X^{2}_{4} = \alpha^2$ we quickly see that we end up with a ...
- 233
6
votes
1
answer
316
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If a fundamental theory exibits e.g. a mirror symmetry, in what sense it the underlying geometry real?
Are the more recently discovered symmetries in string theory such that the theories based on mirroring geometries are absolutely the same from an observable point of view?
I have mirror symmetry in ...
- 8,523
33
votes
10
answers
10k
views
Why do objects follow geodesics in spacetime?
Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation $$\frac{d^{2}x^{\alpha}}{d\tau^{2}}+\Gamma_{\gamma\beta}^{\alpha}\frac{dx^{\beta}}{d\tau}\frac{...
- 3,059
7
votes
3
answers
1k
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Does spacetime in general relativity contain holes?
Are there physical models of spacetimes, which have bounded (four dimensional) holes in them?
And do the Einstein equations give restrictions to such phenomena?
Here by holes I mean constructions ...
- 8,523
1
vote
0
answers
516
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The structure of space-time
I came across this paper recently called The Small Scale Structure of Spacetime and the following idea occured to me:
To uninformed humans the universe appears Euclidean but we know from GR that on a ...
- 297
3
votes
3
answers
3k
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Defining a Riemannian manifold - made easy?
In the context of GTR spacetime, I'm trying to get the basic idea of a Riemannian manifold clear in my mind. Apologies for the longwindedness.
Question 1. Is this a reasonable, simplified summary of ...
- 3,059
37
votes
8
answers
5k
views
Interval preserving transformations are linear in special relativity
In almost all proofs I've seen of the Lorentz transformations one starts on the assumption that the required transformations are linear. I'm wondering if there is a way to prove the linearity:
Prove ...
- 3,732
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
1
vote
1
answer
244
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Can spacetime be defined by the requirement that the physical laws are simple?
When I was student I was told that time is defined by the requirement that the physical laws are simple. For example, in classical mechanics time can be defined by the requirment that the velocity of ...
- 23
6
votes
2
answers
439
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Sewing together flat spacetime pieces = flat spacetime?
I'm trying to imagine the geometry "operations" here:
Angular deficit
and
Curvature of Conical spacetime
If we sew flat spacetime pieces together, what is the requirement for the sewing to not create ...
- 488
18
votes
2
answers
2k
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Can a non-Euclidean space be descripted through an Euclidean space of higher dimension? So why use non-Euclidean?
If you draw a big triangle in Earth 2D surface you will have an approximated spherical triangle, this will be a non euclidean geometry.
but from a 3D perspective, for example the same triangle from ...
- 2,909