The curvature tag has no wiki summary.
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In which direction does space “bend”? [duplicate]
Gravitation is often depicted as a ball on a cloth that curves a hole into space. But in what direction does this hole form? Into the direction the object is moving?
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Does the actual curvature of spacetime hold energy?
My understanding of GR is that curvature of spacetime reflects the density of energy-matter. Does the curvature itself have energy? Or if energy is assigned to curvature it simply reflects the energy ...
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Space time curvature real or theoretical (mathematical)?
Assuming one were in a capsule of some kind, with no window or instruments, and you swung into the gravitational field of a massive object (planet). Assuming no atmosphere to provide friction, could ...
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How can we model intrinsic curvature?
Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?
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What is the curvature of an empty universe?
My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively?
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Changing the scalar curvature (k = 0,+1,-1) with coordinate transformations?
I would like to prove that I can (or can't) change curvature of space, k = 0,+1,-1, via general coordinate transformations, which in principle can mix space and time coordinates together.
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If the universe is 3D, how is space-time like a “fabric”? [duplicate]
I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures ...
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What is the Willmore energy of the Earth (or the geoid)?
Wikipedia defines the Willmore energy as:
$$e[{\mathcal{M}}]=\frac{1}{2} \int_{\mathcal{M}} H^2\, \mathrm{d}A,$$
where $H$ stands for the mean curvature of the manifold $\mathcal{M}$.
What is the ...
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Homogeneous gravitational field and the geodesic deviation
In General Relativity (GR), we have the geodesic deviation equation (GDE)
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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 ...
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1answer
48 views
Parallel transport of a vector along a closed curve in curvilinear coordinates
There is an expression indicating the change of the vector parallel translation along a closed infinitesimal curve in curvilinear coordinates (one way of introducing curvature tensor):
$$
\Delta A_{k} ...
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Spacetime around a Black Hole
If we consider the sun, then space-time is curve around it. My question is that what is the kind of curvature of space and time around the black hole. Is that space and time more curved around the ...
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Curved space to flat space calculation
When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?
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Is there any Calculator capable of calculating and displaying differential geometry? [closed]
Is there any Calculator capable of calculating and displaying differential geometry (display curvature of spacetime)?
$$ds^2~=~g_{ab}dx^adx^b.$$
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Space-time & solar mass
Does the space-time curvature described by Einstein have any affect on the accuracy of our determination in the age of a star or globular cluster? How does this affect our interpretion of how old we ...
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How to calculate a scalar curvature fast? [closed]
Let's have a metric tensor
$$ g^{\alpha \beta} = \frac{1}{\left( 1 + \frac{ct}{R} \right)^{2}}\begin{bmatrix} \frac{1 - \frac{r^{2}}{R^{2}}}{\left(1 + \frac{ct}{R}\right)^{2}} & ...
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Why are we talking about space curvature as if we know what space is? [closed]
1) Why are we talking about space curvature as if we know what space is?
Every question about gravity seems to evoke an answer involving "space curvature" which seems like an undefined placeholder ...
