Do Newtonian Physics help in determining the escape velocity at and inside the event horizon at a distance less than Schwarzchild Radius from the singularity?
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It's true that for a Schwarzschild black hole the radius of the event horizon is at the distance where Newton's law tells you the escape velocity is the speed of light. However you should not let this apparent success lead you into thinking that Newton's law has anything useful to say about black holes. For a start the Schwarzschild radius $r$ is not the same as the radius $r$ used in Newton's equation. We define the Schwarzschild radius as the circumference of a circle drawn round the black hole divided by $2\pi$, so it's what the radius would be if spacetime were flat. If you took a ruler and started trying to measure $r$ you'd get a very different answer.
So, the answer to your question is that Newton's equation is not useful at or within the event horizon, or indeed anywhere where the spacetime curvature is significant.
John Rennie
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There is no 'escape velocity' inside the black hole, the singularity is in the future of all observers crossing the horizon the black hole and is thus unavoidable.
Historically, application of Newtonian dynamics to the light of massive bodies goes back to works of John Michell and Pierre-Simon Laplace (note that light then was thought to be corpuscular, not a wave) in the late 18-th century.
For the overview of this ideas (from the historical viewpoint) see
Montgomery, C., Orchiston, W., & Whittingham, I. (2009). Michell, Laplace and the origin of the black hole concept. Journal of Astronomical History and Heritage, 12, 90-96. online
user23660
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