# Curved space Definition and 9 Discussions

Curved space often refers to a spatial geometry which is not "flat", where a flat space is described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry though some simple cases can be described in other ways. Curved spaces play an essential role in general relativity, where gravity is often visualized as curved space. The Friedmann-Lemaître-Robertson-Walker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe.

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1. ### I How do gravitational fields transform under a boost in velocity?

Let's say we have some observer in some curved spacetime, and we have another observer moving relative to them with some velocity ##v## that is a significant fraction of ##c##. How would coordinates in this curved spacetime change between the two reference frames? For example, imagine a...
2. ### A Lense-Thirring effect - General Relativity

Let us assume a "toy-metric" of the form $$g=-c^2 \mathrm{d}t^2+\mathrm{d}x^2+\mathrm{d}y^2+\mathrm{d}z^2-\frac{4GJ}{c^3 r^3} (c \mathrm{d}t) \left( \frac{x\mathrm{d}y-y\mathrm{d}x}{r} \right)$$ where ##J## is the angular-momentum vector of the source. Consider the curve  \gamma(\tau)=(x^\mu...
3. ### A Orbital Angular momentum couples to Christoffel connection

I am trying to understand Wen and Zee's article on topological quantum numbers of Hall fluid on curved space: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.69.953 They passingly mentiond the fact that a spinning particle with orbital angular momentum $s$ moving on a manifold with...
4. ### I Why do planets follow the same curvature at both foci?

We are told that planets and comets orbit the sun in an ellipse (Kepler's 3 laws) as shown below: We are also told that according to Einstein's theory of gravity, there is no force applied. Implied is that the planets move in straight lines through curved space. We know that the effect of...
5. ### I If there are gravitons, is space not curved?

If gravitons are proven to exist, would that mean space is not curved?
6. ### Curved space?

Hello, I just joined. I have no formal background in physics, just curiosity. So, my questions may well be simplistic to most of you. Hopefully, that is permissible, now and then! First question, if space, as it's usually defined, is empty, nothing, how can it be curved? Hankb
7. ### Does light curve toward ordered

If I'm correct in thinking light curves towards objects with less entropy; why wouldn't the path of least resistance be towards entropy?
8. ### Hubbard-Stratonovich transformation

Can one apply the Hubbard-Stratonovich transformation to the exponential of the Laplace–Beltrami operator?
9. ### Gyros behaving in the space close to a massive object

Given an object spinning on its own axis, in orbit around a planet with mass and that the object is traveling in the direction of its axis, does the axis continue to point at the same point in infinity as it rotates around the planet or does the axis follow the curvature of space around the...