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awarded  Nice Question
May
21
comment Manifolds, unit 2-sphere and stereographic projection
BTW you can choose more than 2 if you like. Say you break the range of $\theta$ $[0,\pi]$ into 10 intervals $[0,\pi/5),(\pi/10,3\pi/10)...(4\pi/5,\pi]$ (notice these sets overlap - you need that for technical reasons. They can't "just touch"). Then you would have 10 strips, each with values of $\phi$ that run 0 to $2\pi$. Each point is in at least one, and they cover $\mathbb{S}^2$.
May
21
comment Manifolds, unit 2-sphere and stereographic projection
I hope my edit(s) cleared it up. You remove one point (say, $\theta=0$) from one coordinate chart, and you remove the other ($\theta=\pi$) from the second coordinate chart. Now you have two charts which are everywhere invertible and every point ${(\theta,\phi)}$ of the sphere is included in at least one of them.
May
21
revised Manifolds, unit 2-sphere and stereographic projection
I was mislead by the way the question was asked, but it should be more clear now.
May
21
answered Manifolds, unit 2-sphere and stereographic projection
May
21
comment Can't derive FRW Christoffel symbol
Just a minor comment, because I see it a lot. $g^{\sigma\rho}=1/g_{\sigma\rho}$ is easy to write, but depending on what index notation you are using (component or abstract), it may be nonsense. If you mean that "each component of this particular tensor is 1 / ( the component of this other particular tensor )", then I'm fine, but that's only true for the metric if the metric is diagonal. The real relation is $g^{\sigma\rho}g_{\sigma\rho}=1$, true in both abstract and component notation.
May
19
answered Do holes have physical existence?
May
19
answered Is the time “direction” in General Relativity equivalent to a spatial volume
Apr
29
awarded  Taxonomist
Apr
29
answered Layman's explanation and understanding of Einstein's field equations
Apr
29
comment Can a perfectly mathematically describable universe exist in a multiverse?
I'll leave the answer, but yeah it's no longer very applicable.
Apr
29
answered Can a perfectly mathematically describable universe exist in a multiverse?
Apr
27
comment Will a ferromagnet retain its magnetic properties after reaching the curie point?
just wanted to add a video which clearly demonstrates this effect: youtube.com/watch?v=mUz1ZaIHvDs. This is done in the field of a strong Neodymium magnetic so that the field can be recreated once the sample (Ni here) cools down.
Apr
27
comment How realistic is a “bolas” system for artificial gravity in space travel?
might be even more fun to consider two very massive pods orbiting around each other under the force of gravity. Then you have no need for the rope at all :-)
Apr
17
answered How GR, QFT, or string theory address the one-directional feature of time?
Apr
2
comment What would it take to cause lightning to jump between the Moon and the Earth?
Right, it's not easily calculated, which is why I choose the Schwinger limit. It might be something like an upper bound to this whole thing, I agree, but without some effective theory/time to worry about the interplanetary medium, I wanted something concrete to hold onto.
Apr
2
comment What would it take to cause lightning to jump between the Moon and the Earth?
I agree, the estimate may not be great but it's based on my assumption of total vacuum, and the lack of microscopic details of the physics involved.
Apr
1
revised What would it take to cause lightning to jump between the Moon and the Earth?
added 11 characters in body
Apr
1
revised What would it take to cause lightning to jump between the Moon and the Earth?
Expanding the answer, as promised.
Apr
1
revised What would it take to cause lightning to jump between the Moon and the Earth?
Expanding the answer, as promised.