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13

I think the essential problem lies in the difference between the mathematical meaning of curvature, and the way in which we actually describe a manifold, or a curved space (or spacetime). Although we describe the universe as having spacetime curvature (which is mathematically true), curvature refers to the Riemann curvature tensor, which is a rank-4 tensor, ...


8

The spacetime metric of a spatially-flat Friedmann universe — like ours seems to be, on the largest scales — is $$ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2)$$ where the function $a(t)$ is the Friedmann scale factor describing the expansion of space as a function of cosmological time $t$. You can calculate its 4D Riemann curvature tensor $R_{\mu\nu\lambda\kappa}$ and ...


5

The notion of "spatial curvature" only makes sense when the spacetime geometry is symmetric enough that there is a natural/preferred foliation of it into spacelike slices. You can then talk about the intrinsic curvature of those slices. The easiest way to understand why the curvatures can be different is to look at a toy cosmological model, like ...


2

My question is: is gravity, in the modern sense, viewed as a force arising the metric field, or do we stick to the original GR: gravity being curvature of spacetime? One has to keep in mind that physics is modeled by several different theories, very successfully. Thermodynamics, statistical mechanics, Maxwell's equations for classical electromagnetism, ...


2

Interesting idea, but ... no. It does not work like that. The branching idea is a bit misleading. Instead, the Many Worlds interpretations refers to the terms in the superposition of the wave function of the universe. Each terms in this superposition is viewed as a "world," which is perhaps a bit misleading. So all possible "worlds" are ...


1

General relativity is, unfortunately (or fortunately, depending on your perspective), a lot more complicated than that. The curvature of space-time is directly related to the stress-energy tensor, which, roughly speaking, is a 4x4 matrix that encapusaltes the ideas of energy, momentum, and stress (the rate of flow of momentum) into one object.


1

Electromagnetic effects propagate in free space at the speed of light, so an object at point A sees the electromagnetic field from another object at point B only after the time interval that a light wave takes to travel from B to A. The same is true of gravity, because gravitational effects also propagate at the speed of light.


1

It follows from the theory of relativity that time is not the same everywhere. Basically, time moves slowly with an increase in gravity and an increase in speed as well. Thus, you would age slowly if you are close to a black hole or traveling at speeds close to the speed of light. I would suggest you to go through the following blogs to understand this ...


1

It all has to do with gravity. The stronger the gravity the slower the time. According to this article the earths surface is 2 1/2 years older than the earths core because of a difference in gravity. https://www.sciencealert.com/earth-s-core-is-2-5-years-younger-than-its-crust-thanks-to-the-curvature-of-space-time


1

An outside observer sees events (such as the vibrations of a light source) occurring more slowly deep in a strong gravitational field. We may see the the stars orbiting the dense center of the galaxy as going slower than expected.


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