Linked Questions

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General Relativity and cosmology [duplicate]

What is the physical meaning of Ricci scalar is a covariantly constant?
10
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4answers
2k views

Why do we say “Spacetime Curvature is Gravity”?

Although "Spacetime Curvature is Gravity" is the first statement that is told to an infant by the "popular science", I believe that really really misrepresents what GR has to say. I am posting this ...
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5answers
1k views

What would happen if the light-speed was higher? [closed]

I came across a rather interesting passage in a book attempting to debunk Darwin's Theory of Evolution from a Christian viewpoint. One thing the book suggested, was that various scientific ways to ...
5
votes
2answers
7k views

What does the Ricci tensor represent?

I'm new to this site so I am sorry if I get the format wrong. However, I'm having some trouble understanding the Ricci tensor. I know it is found by contracting the Riemann tensor and that this is ...
12
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2answers
2k views

What is the geometrical interpretation of Ricci tensor?

In differential geometry and general relativity space is said to be flat if the Riemann tensor $R=0$. If the Ricci tensor on manifold $M$ is zero, it doesn't mean that the manifold itself is flat. So ...
2
votes
3answers
6k views

What is a Christoffel symbol?

What is a Christoffel symbol? I often see that Christoffel symbols describe gravitational field and at other times that they describe gravitational accelerations. Then, on some blogs and forums, ...
2
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3answers
1k views

What is the physical meaning of the Levi-Civita connection?

I'm taking a course in General Relativity and I have studied the fundamental theorem of Riemannian geometry: Let $M$ be a manifold with metric $g$. Then exists an unique torsion-free connection $\...
6
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1answer
2k views

Interpretation of the Weyl tensor

My question arises from the interpretation of Ricci curvature. If I am not mistaken : The Ricci scalar measures the change of volume of small geodesic balls, compared to a euclidean space, it is a ...
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3answers
424 views

What is the physical meaning of the components of the affine connection in General relativity?

What is the physical meaning of the components of the affine connection in General relativity? I read in a GR book that the connection describes the gravitational field, so what does each of its ...
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2answers
505 views

Can anyone explain the Ricci curvature? [closed]

I am 13 years old and love physics. Can anyone explain simply what it is?
3
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1answer
423 views

Physical visualisation of curvature

I was wondering-how do you visualise curvature in the context of general relativity. The gravity well and trampoline analogies are quite wrong, so I want a more realistic approach to it (say, the way ...
0
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1answer
233 views

Does spacetime curvature (for time dilation) cancel out at the point of center of mass (because curvature effects cancel out from all directions)? [duplicate]

I have read this question and John Rennie's answer to it: How does "curved space" explain gravitational attraction? I am asking about the time dilation affects of it, I am not asking about ...
3
votes
1answer
227 views

(Scalar) Ricci flatness of a metric

What is the physical meaning to vanishing Ricci scalar $R=0$ of a metric in general relativity? Note that this is not the same questions as the geometric meaning of $R_{\mu\nu}=0$ which has been asked ...
3
votes
1answer
209 views

Difference between curvature and Ricci scalar curvature?

I know about curvature by this notation $$\tau=\frac{dt}{ds}$$ the change of tangent vector with respect to arc length $s$ . I also know about Ricci scalar curvature is $$g^{ij}R_{ij}=R$$ I know ...
1
vote
1answer
66 views

Geometrical interpretation of curvature invariants

Consider a Riemannian manifold. It is possible to describe it by curvature invariants. Now, is there any geometrical description (intuition) for simple invariants such as scalar curvature, Ricci ...