# 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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### Does gravity CAUSE the bending of spacetime, or IS gravity the bending of spacetime? [closed]

In reading these discussions I often see these two different definitions assumed. Yet they are very different. Which is correct: Does gravity CAUSE the bending of spacetime, or IS gravity the ...
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### Inertial and gravitational Mass

Why definition of mass is not stated as " the property of object to change radius of curvature of space time fabric is called mass"
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### Example of a Riemannian metric in $(1+1)$D by oscillating geodesics

Newtonian gravitational potential for one mass gives oscillating motions to test particles. Can a somewhat similar movement be produced by ($2$-dimensional $+-$) curvature? I mean an explicit metric ...
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### Relation between curvature and metric determinant

This is my first question so please let me know if I'm asking my question appropriately! I've been trying to build up an intuition for what curvature of spacetime represents physically. Mostly I have ...
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### If the space-time curve was quantified and has a mathematical function what would the derivative of the function mean? [closed]

Say I have a massive object: This object as we know causes spacetime to bend and curve. The "maximum curve" which I would define as the line in space time that runs directly through the center of ...
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### Do shapes of matter affect space-time distortion?

We know heavy objects bend space-time, but does the curvature only depends on the mass? Or different shapes bend space time differently?
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### Can image method (method of image charges) of electrostatics be used for curved surface?

Suppose we have a fixed point charge in front of a half cylinder. Can we find energy of system using this method? If so, how? I have seen image method being used for infinite sheets. Can we use it if ...
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### Is it accurate to say space moves because spacetime is curved?

I've learned from PBS Space Time videos that space rushes into a black hole's event horizon at the speed of light. I'm trying to square this with the analogy of stretched rubber sheet everyone uses; ...
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### Equivalence principle and bending of a light ray

In some explanations of a phenomena of curved spacetime we have an example of a light ray emitted in a freely falling space ship perpendicular to the direction of a free fall. In this case, for an ...
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### How is time affected by the bending of space-time?

By Newton's Laws, we can calculate the effect of gravity, but he didn't give the actual reason for gravity. I searched the internet for it, but all the answers have this "bending of space-time" stuff. ...
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### How to derive the formula for the second covariant derivative?

If the first covariant derivative is derived by taking the partial derivative of a vector and applying the product rule to the vector components and the vector bases, couldn't the same thing be done ...
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### What generates the curvature which is necessary for curling-up extra dimensions?

To say it right away, I am not an expert in string theory, but I know well General Relativity. So I wonder how the curling up of extra-dimensions which is assumed in many "Kaluza-Klein" like theories (...
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### If an object is heated, does the curvature of the object at a point effect how heat flows out at that point?

For example: while expediting, I have to move little football/oval shaped bowls containing food. I want to hold it in such a way that, when moving it from station 1 to station 2, I have the least ...
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### How to explain curvature of spacetime at the time of big bang [duplicate]

According to Einstein mass causes curvature of spacetime ,so he basically defined mass using space i.e (mass is something which causes curvature of spacetime).Now at the time of bigbang there was no ...
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### A simple way to measure the shape of warped spacetime

Background I've wondered for years about ways to visualize how mass (and hence gravity) affects the curvature of spacetime. The 'bowling ball on a rubber sheet' while being useful for the simplest ...
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### Visualising/getting inuition for, the manifold resulting from these geodesics?

This is related to another post of mine. I know that the geodesics for flat Euclidean Space are straight lines. But I want to take these curved geodesics and tried to work backwards to determine the ...