All Questions
Tagged with spacetime differential-geometry
71
questions
161
votes
6
answers
55k
views
Why would spacetime curvature cause gravity?
It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" ...
- 1,926
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
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
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
29
votes
5
answers
6k
views
Does curved spacetime change the volume of the space?
Mass (which can here be considered equivalent to energy) curves spacetime, so a body with mass makes the spacetime around it curved. But we live in 3 spatial dimensions, so this curving could only be ...
- 421
18
votes
2
answers
2k
views
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
29
votes
4
answers
5k
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 ...
user1532
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
4
votes
2
answers
619
views
Can we just take the underlying set of the spacetime manifold as $\mathbb{R^4}$ for all practical purposes?
In mathematical GR and also in some informal GR presentations (eg: MTW), manifolds are always mentioned before talking about GR... but now I am starting to wonder.. if it even actually neccesary?
In ...
- 7,980
4
votes
3
answers
691
views
Why does GTR not need a higher dimension to describe the bending of spacetime?
I am a bit confused on how GTR uses intrinsic curvature instead of extrinsic curvature. Maybe it is just a misunderstanding, but I will do my best to describe my question:
If we take an object of $n$ ...
- 3,778
15
votes
0
answers
272
views
Is it known what the necessary and sufficient conditions are for the existence of a "3+1 split" (by means of a foliation) of a (Lorentzian) manifold?
When trying to do physics on a more general pseudo-Riemannian manifold we want to require that there is a foliation of this manifold into three-dimensional subspaces. By this I mean we would like to ...
- 301
6
votes
2
answers
433
views
Confusion regarding bundle structure of Galilean spacetime in Penrose's The Road to Reality
I am reading Roger Penrose's The Road to Reality. In section 17.3, I encounter the following passage. To give a context, Penrose was explaining that even though an Aristotelian spacetime can be ...
- 682
4
votes
3
answers
5k
views
What is the physical meaning of the Eddington-Finkelstein coordinates?
What is the physical meaning of the Eddington-Finkelstein coordinates? I want to see a some physical process (experimental) that could explain the many transformations of coordinates into this ...
- 5,794
3
votes
1
answer
484
views
Kleppner derivation of Lorentz transformation
I am reading Kleppner.(Lorentz transformations)
He said,we take the most general transformation relating the coordinates of a given event in the two systems to be of the form
$$x'=Ax +Bt,
y'=y,
z'=z,
...
- 3,455
16
votes
5
answers
5k
views
Does space curvature automatically imply extra dimensions?
Total newbie with basically no physics knowledge here :) I would welcome any correction to the steps of my reasoning that lead to my question, which could easily turn out to be invalid :)
My current ...
- 271