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World map from China, first time I see this projection (files.catbox.moe)

submitted 1 month ago by [email protected] to c/[email protected]

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[–] [email protected] 1 points 1 month ago* (last edited 1 month ago)

Black holes are actual singularities (by existing physics), though, not mere coordinate singularities like the poles. Coordinate singularities show up in GR too, but you can get rid of them by changing your coordinate system - a very common operation, apparently.

You're right the math is similar; you can learn a lot of differential geometry concepts just by looking at coordinates of, or projections onto a sphere. Curvature gets exponentially more complex as you step into 3 and then 4 dimensions, but the same mathematical objects apply.

(Interestingly, differential geometry in dimensions 5 and up is the same as in 4, and topology actually gets easier)