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### Why isn't an infinite, flat, nonexpanding universe filled with a uniform matter distribution a solution to Einstein's equation?

In Newtonian gravity, an infinite volume filled with a uniform distribution of mass would be in perfect equilibrium. At every point, the gravitational forces contributed by masses in one direction ...
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### Is there a limitation on Gauss' law? [duplicate]

Recently I had a question to find the electric field at a distance $R$ from the origin, where the space is filled with charge of density $\rho$. I did this by assuming a Gaussian surface of radius $R$....
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### Anti-gravity in an infinite lattice of point masses

Another interesting infinite lattice problem I found while watching a physics documentary. Imagine an infinite square lattice of point masses, subject to gravity. The masses involved are all $m$ and ...
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### Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get \phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty \...
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### Gravitation in a space that is topologically toroidal

In my scant spare time I'm building an Asteroids game. You know - a little ship equipped with a pea shooter and a bunch of asteroids floating around everywhere waiting to be to blown up. But, I wanted ...
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### Fulvio Melia's linear cosmology

I would be interested in what people think of Fulvio Melia's argument for a linearly expanding Universe. I realize that the experimental evidence seems to be pointing to an accelerating Universe but ...
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### Infinitely many planets on a line, with Newtonian gravity

(I apologize if this question is too theoretical for this site.) This is related to the answer here, although I came up with it independently of that. $\:$ Suppose we have a unit mass planet at each ...
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### Finite or ∞ set of masses & ∃ gravity center?

Any finite & non empty set of masses has a computable center of gravity: $\vec{OG} = \frac{\sum_i m_i \vec{OM}_i}{\sum_i m_i}$ . Does the contrapositive permits to conclude that a mass system ...
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### What would happen if we had a crystal structure but only gravitational interactions?

The idea is simple. Let's say we arrange similar bodies (call them planets, ions, anything) in an infinite crystal structure, but the only possible interactions are gravitational interactions. A ...
Imagine there's a sphere of radius $R$ which has constant density $\rho$ and you can stand anywhere inside of the sphere. Wherever you stand within the sphere, you'll only feel gravity coming from the ...