When is a test mass not captured by a black hole?

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The force on a test mass m near a black hole of mass M is

$$F (r)= \frac{GMm}{r^2\sqrt{1-\frac{2GM}{rc^2}}}$$

$F (r)= \frac{GMm}{r^2\sqrt{1-\frac{2GM}{rc^2}}}$

When is a test mass free to leave to infinity?

Or equivalently: what energy at distance r is sufficient for the test mass to escape?

I have not found an answer with Google scholar - but I may have searched in the wrong way.

asked Jan 20, 2022
recategorized Jan 22, 2022

Chandrasekhar "The Mathematical Theory of Black Holes", Chapter 3 on Schwarzschild space-time may be helpful here. As may be the relevant chapter in "Gravitation" by Misner, Thorne, Wheeler. And I am rather sure there are further helpful books on the issue.

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