All Questions
6
questions
1
vote
0
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102
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What is a hypersurface?
What is the concept of hypersurface in general relativity? I know it could be characterized into three categories but how do we define hypersurface (in general) in physics? I didn't get what thing it ...
- 59
5
votes
1
answer
1k
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What does Penrose mean when he talks about topology of spacetime?
Let us now set aside the question of the submicroscopic structure of space-time and concentrate, instead, on its large-scale properties. In this case, we may imagine that the smooth manifold picture ...
- 7,980
0
votes
1
answer
197
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How do 'locally Euclidean' and 'Lorentzian' requirements in manifolds reconcile?
In GR, we define our manifolds to be locally Euclidean. However, we also demand that our metric tensor have a Lorentzian signature. Since the metric tensor is a measure of curvature, doesn't the first ...
- 579
8
votes
4
answers
992
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Definition of spacetime in GR: what is the underlying set of the spacetime manifold?
In all the references/textbooks that I have looked at, the precise definition of spacetime is never really clear. By gathering the hypothesis that we need to make, I get the following definition: $$\...
- 1,044
4
votes
1
answer
237
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Definition of $i^+,i^-,i^0, \mathscr{I}^+,\mathscr{I}^-$ in a general spacetime
I've seem sometimes a construction being carried out specificaly in Minkowski spacetime:
One picks the standard metric tensor $$g = -dt^2 + dr^2 + r^2 d\Omega^2$$
an introduces two new coordinate ...
- 36.5k
1
vote
2
answers
1k
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What is a geometrical object?
From the Wikipedia link for Geometry:
Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position ...
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