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May 20, 2022 at 14:52 comment added ProfRob Is this only true for radial motion?
Sep 14, 2019 at 9:59 comment added jinawee After coming back to this question, your answer is valid for a Schwarzschild BH when the escaping particle travels radially and you measuring the speed from the starting point. The formula I wrote assumes you measure the distance from a point at infinity, which is not the same since speed is coordinate dependent.
Aug 15, 2017 at 21:29 comment added jinawee I don't buy your derivation. The energy of a particle is not given by the second formula you've written since it neglects the gravitational field, you are considering a free particle. The correct energy is $E=\gamma mc^2 \sqrt{1-2GM/R}$, which leads to $v_e=\sqrt{2GM/R - (2GM/R)^2}$.
Aug 11, 2012 at 20:24 comment added voix @AlanSE - Yes, for a point-like object.
Aug 11, 2012 at 12:36 comment added Alan Rominger So the escape velocity at the event horizon would go to the speed of light as the ratio in the radical goes to 1? Am I reading that right? That would still quite simply imply infinite energy, so it seems consistent.
Aug 10, 2012 at 22:21 history edited voix CC BY-SA 3.0
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Aug 10, 2012 at 22:08 history answered voix CC BY-SA 3.0