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Homework Statement:
 Calculate the time it takes for an object with some initial (vertical) velocity to fall towards a black hole from r_0 to r_1. Include relativistic effects.
Homework Equations:

(1) F = ma/(1u^2/c^2)^(3/2)
(2) F = GmM/r^2
(3) Energy = Potential + Kinetic
First of all, this isn't homework, so I'm not sure if this is the appropriate channel to post this in. I study physics as a pastime and I simply want to know how to solve this problem. I'm willing to do all of the work, or none of it, as long as I understand the solution!
Because the object is close to a massive body we need to assume that the gravitational acceleration changes with r. Integration is involved.
Because we want to account for Relativity, I *think* equation 1 is the appropriate formula.
An associate suggested that I use the conservation of energy (3). Calculate the gravitational potential at each height, calculate initial kinetic energy, then we will know final velocity. I believe at that point we can solve for t...somehow...
Any insight would be greatly appreciated!
Because the object is close to a massive body we need to assume that the gravitational acceleration changes with r. Integration is involved.
Because we want to account for Relativity, I *think* equation 1 is the appropriate formula.
An associate suggested that I use the conservation of energy (3). Calculate the gravitational potential at each height, calculate initial kinetic energy, then we will know final velocity. I believe at that point we can solve for t...somehow...
Any insight would be greatly appreciated!