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This post is part of a series of older, now mostly-missing posts, in which I shared math/physics concepts I thought were cool. I was 14/15 when I made them (this was 2021), so a lot of them are not very good, but I'm reuploading them here for posterity's sake (plus, I don't post about physics nearly enough on here, for being a main focus of this site (>_>) I have also preserved their formatting as best as I can, even if that formatting isn't the best either.
Fun fact - Any event measured in a black hole will never be seen from outside!
this is because the radius a black hole takes its affect (i.e, where gravity is so strong light cannot escape) is derived by
![\[\frac{1}{2}mv^2=\frac{GMm}{r}\]](/pics/equations/sr1.webp)
which, at the speed of light evaluates to
![\[r=\frac{2GM}{c^2}\]](/pics/equations/sr2.webp)
this is called the Schwarzschild radius!
how does this mean you can see events going on in a black hole?
Well, due to relativity, spacetime is bent by gravity, yielding
![\[c^2\tau^2=(1-\frac{r_{schwarz}}{r})c^2dt^2-\frac{dr^2}{(1-\frac{r_{schwarz}}{r})}-r^2d\Omega\]](/pics/equations/sr3.webp)
when r = the swarzschild radius, the dt² term goes to zero....
...while the second term goes to infinity
so the time for an avent within the schwarzschild radius takes would INFINITE (actually neagtively infinite but idk how that would go so maybe i just effed up my notes lol)
tldr: go in blackhole go byebye