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Questions tagged [curvature]

Use this for questions pertaining to curvature of manifolds. Does not need to be specific to general relativity, but also for curvature of e.g. a [tag:calabi-yau] manifold.

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1answer
928 views

What is the difference between Ricci curvature tensor and the Laplacian

Can someone please explain the difference between the information that the Ricci curvature tensor gives us and that which the Laplacian offers? Here is my shot at it: My concept of the Ricci ...
8
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0answers
446 views

Why does the overhand knot jam but the figure-8 knot doesn't?

After tensioning a rope with an overhand knot in it, it is often very hard if not impossible to untie it; a figure-8 knot, on the other hand, still releases easily. Why is that so? Most "knot and ...
14
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4answers
4k views

ALL “forces” as manifestations of properties of space-time

I apologize if this seems like a quack question, but I need some insights by those who know much more than me in Physics. Anyway, the gravitational "force" (not really a force) is a manifestation of ...
6
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4answers
2k views

The Sun as a gravitational lens

Since the Sun is a gravitational lens with as focal length of 550 AU for visible light, with an immense amplification factor, shouldn't it light up objects hanging out there? We should get solar ...
8
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1answer
401 views

Curvature of the Universe imaginary?

If the curvature of the universe is zero, then $$Ω = 1$$ and the Pythagorean Theorem is correct. If instead $$Ω> 1$$ there will be a positive curvature, and if $$Ω <1$$ there will be a negative ...
4
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3answers
6k views

Ricci scalar for a diagonal metric tensor

I was wondering if there is a general formula for calculating Ricci scalar for any diagonal $n\times n$ metric tensor?
5
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2answers
473 views

How is the shape of the universe measured by scientists?

I would like to learn how scientists go about measuring the large-scale curvature of the universe to determine if the universe is closed 'i.e. spherical', flat, or open 'i.e. saddle shaped'. My ...
5
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1answer
1k views

A question about surface tension of membranes and their curvature

I'm reading a review about membranes properties and I have reach a section about fluid membranes. The section discuss the principal curvatures ($c_1, c_2$) and the spontaneous curvatures ($c_0$). ...
56
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14answers
125k views

What is the simplest way to prove the Earth is round?

Assume you've come in contact with a tribe of people cut off from the rest of the world, or you've gone back in time several thousand years, or (more likely) you've got a numbskull cousin. How would ...
10
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2answers
638 views

How can a point-like particle “feel” gravity, if locally the curvature of spacetime is always flat?

I imagine a point-like particle can only experience the local properties of spacetime. But locally there is no curvature and no gravity, as it is often stated that Locally, as expressed in the ...
-2
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1answer
475 views

Space-time hospitality

Are there any reasons to assume that organic processes cannot arise in relatively flat spacetime environments? An argument for the existence of a critial value or window.
5
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5answers
2k views

How does the curvature of spacetime induce gravitational attraction?

I don't know how to ask this more clearly than in the title.
28
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6answers
5k views

Does the curvature of spacetime theory assume gravity?

Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form "gravity wells." Objects which are ...
3
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3answers
369 views

asymptotic curvature of the universe and correlation with local curvature

There is not-so-rough evidence that at very large scale the universe is flat. However we see everywhere that there are local lumps of matter with positive curvature. So i have several questions ...
65
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12answers
53k views

How exactly does curved space-time describe the force of gravity?

I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or ...
43
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4answers
12k views

What is the physical meaning of the connection and the curvature tensor?

Regarding general relativity: What is the physical meaning of the Christoffel symbol ($\Gamma^i_{\ jk}$)? What are the (preferably physical) differences between the Riemann curvature tensor ($R^i_{\ ...
25
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3answers
7k views

Nature of gravity: gravitons, curvature of space-time or both?

General relativity tells us that what we perceive as gravity is curvature of space-time. On the other hand (as I understand it) gravity can be understood as a force between objects which are ...