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What was the incorrect reasoning?



I can't say for sure on this particular case, but the usual reasoning is this:

Using Newtonian Mechanics (I'll skip the derivation.) you can calculate escape velocity as follows: v = sqrt(2GM / r)

r is the distance to the center of mass, G is the usual gravitational constant and M is the mass of the body.

So, now we can reason about an object whose escape velocity is c.

c^2 = 2GM / r and rearranging a bit:

r* = 2GM / c^2.

Thus, IF we packed a mass M into the radius r*, we would have a Newtonian blackhole.

It turns out, quite incredibly, that this r* is in perfect agreement with the swarzchild radius from a non-rotating blackhole calculated using general relativity. Exactly why these two are in such agreement has never been explained to me other than as a coincidence. But it's quite incredible since usually r^3 terms pop up prior to the event horizon (at the same radius) which make GR make different predictions about orbits. (Such as the precession of mercury)


Doesn’t GR always agree with Newtonian gravity when objects aren’t accelerating?



What's "not accelerating" about going in an ellipse? Doesn't that imply constant (and varying) acceleration?




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