# 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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### How to prove that a flat spacetime admits Minkowski coordinates?

How should I prove the following in general relativity? A flat spacetime can be covered by Minkowski coordinate neighborhoods. A flat spacetime with the trivial topology can be covered by a global ...
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### What does it mean that spacetime is curved? [closed]

I am not sure whether this is a physics question, a maths question or even a linguistics question; please forgive me if I have chosen the wrong platform. I am trying to understand what it really means ...
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### Physical differences between our universe and strongly negatively curved one

Interestingly, the idea of a negatively curved universe isn't entirely science fiction. In particular if decrease a single physical constant (known as the density parameter) to be less than one, the ...
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### How does electromagnetism work in a negatively curved universe?

Let's say that there was a negatively curved universe (in particular $\Omega < 1$). I assume that means the universe would be like Hyperbolic space. In our universe, electromagnetism obeys an ...
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### Is Flatness Problem still a problem since the observable universe is flat but the whole universe can be curved on much larger scale?

When we say the universe is flat, we mean just the observable universe. So that doesn’t mean the shape of the whole universe is also flat (ie. it can be curved on much larger scale) Is Flatness ...
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### Can a 2D universe be closed?

Consider a universe as a curved 1D line looped onto itself. The second dimension is time. On one hand, this line is easy to visualize as a circle embedded in a flat 2D plane. However, there is only ...
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### Could LIGO have detected R'lyeh if it existed?

In Possible Bubbles of Spacetime Curvature in the South Pacific, that R'lyeh might be exist within a bubble of spacetime. (It appears to be a joke paper since some of the references are fictional, but ...
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### A problem with how curved spacetime explains gravity [duplicate]

I've read quite a few online explanations of how curved spacetime is the reason objects are drawn to each other, and that gravity is an illusion. Most of them follow the same path: explain what ...
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### Does CFT in AdS/CFT live in flat spacetime?

As the title says, does CFT in AdS/CFT live in flat spacetime, or is it only approximately flat?
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### Curved Space and Great Circles in General Relativity

I have been studying general relativity by B. Schutz. It says locally straight lines on a sphere does not remain parallel, as great circles do intersect on a sphere. Below is a picture where two ...
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### 1+1D curved spacetime diagram example

This is a very basic question about General Relativity. I haven't take any GR course yet. Suppose a flat spacetime with one space direction and one time direction, as follows: Now add a mass at rest ...
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### 2D Liouville Stress-Energy tensor

I am working on 2D Liouville field theory and trying to follow mostly Harold Erbin's note on 2d quantum gravity and Liouville theory. I have a really simple question: One consider the Euclidean ...
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### Can I state that a spacetime is homogeneous and isotropic iff $\nabla_\mu R = 0$?

If a spacetime is homogenous and isotropic can I say that $\nabla_\mu R =0$? I was reading this paper https://arxiv.org/abs/astro-ph/0610483 and, I think that is the justification for the authors ...
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### A star with its radius not much larger than its Schwarzschild radius

I was asked about the question today: suppose that you are observing from afar a spherically symmetric star of mass $M$. Its radius $R$ is $\textbf{not}$ much larger than its Schwarzschild radius. ...
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### The commutation of partial derivatives in curved spacetime

While following a lecture series on General Relativity, an argument was presented that in order the spacetime to be flat, a vector parallel transported along two different paths should yield the same ...
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### Intuition for why mass and energy curve the space-time fabric and for why this relationship is linear?

The force of gravity does not exist I understand(-ish) that, following general relativity, an apple falls onto earth, not because there is a force pulling earth and the apple toward each other but ...
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### Riemann tensor and the non-commutativity of parallel transports

Riemann curvature s denoted by $R^a_{bcd}$. If you try to attempt to parallel transport a tangent vector $\psi$ along an infinitesimal parallelogram given by two tangent vectors along non-parallel ...
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### Contribution of the metric tensor towards the Riemann curvature tensor

If I specify a metric tensor in terms of a choice of bases in the co-tangent space at a given point in a manifold, how much information does the metric tell me about the curvature tensor at that point?...