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Schwarzschild Black Holes

One of the interesting features of general relativity is that time slows down as you approach the Schwarzschild radius of a black hole. Not to you, of course; your subjective experience of time is unaffected, but an outside observer would see your clock moving slower and slower (and turning redder and redder) as you fell into the black hole, until (paradoxically) you stopped completely (and were red-shifted out of sight) at . Your own experience would depend upon the mass of the black hole. If it were big enough, the trip in free fall through would be rather uneventful - you wouldn't notice much of anything unusual, unless of course you tried to get out again. If, on the other hand, you approached a small black hole, the tidal forces [the gravitational gradient ] would tear you apart before you even reached . This has some interesting consequences which I will discuss later.

The transformation between "outside" and "inside" coordinates has an interesting feature: while it is strictly impossible for anything inside to come out, one can imagine extending the mathematics of the relativistic transformation from outside to inside, at least formally. The result would be that "inside time" is in the opposite direction from "outside time." This would mean that what we see as matter falling inexorably into a black hole must "look" to the interior inhabitants (if any) like an expansion of matter away from the singularity - a sort of Big Bang. Which raises an interesting question about our Big Bang: are we inside a black hole in someone else's Universe? Hmm.... And are the black holes in our Universe time-reversed Big Bangs for the inhabitants (if any) of their interiors? Hmmmmmm.... Unfortunately, this sophistry is probably all wrong. If you want a proper, correct and comprehensible description of phenomena at the Schwarzschild radius, go talk to Bill Unruh!



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Jess H. Brewer - Last modified: Mon Nov 23 16:41:52 PST 2015