Set v = c to obtain Schwarzchild radius. https://en.wikipedia.org/wiki/Schwarzschild_radius …
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The gravitational field at the event horizon is not necessarily strong. Solve the problem for an extremely large black hole and then use analytic continuation.
you can't get GR from analytic continuation of newtonian mechanics
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also at the event horizon there are plenty of relativistic effects not accounted for by newtonian mechanics (e.g. time dilation upon crossing etc).. black holes need to be treated relativistically
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No. You are thinking small black holes. Very, very big ones don't even have significant tidal effects. The biggest known (the entire Universe) is flat (total energy exactly zero.)
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My point is that you can solve for the escape velocity of a black hole so large that the gravity at the event horizon is as small as you want it to be. And the formula is the same for all r, not just in the limit. So, GR can at best change the result by a factor or 1+epsilon.
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But you can get the constant that dimensional analysis cannot infer. My point is that the form of the equation for the SR is neither coincidental or misleading. It follows from conservation of energy and equivalence principle.
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