1. The problem statement, all variables and given/known data An object falls radially towards a non rotating black hole from infinity (i.e. the velocity is the same as the escape velocity except negative). The black hole has a Schwarzschild radius of Rs = 2GM/c2 where G is the gravitational constant, M is the black hole's mass and c is the speed of light in free space. The object has mas m and velocity v = dr/dt where r is distance from the centre of the black hole and t is time. When I calculate the momentum, I can get either a positive or negative result, depending on how I do it, since a square root is involved. I know it should be negative so in this case and in general,how can I be sure I have the right root? 2. Relevant equations According to a website I looked up, the velocity should be: dr/dt = (+/-) sqrt(M/r)(1-Rs/r) However i believe that M=1 & c=1 in their cauculations. Adding them back in gives: dr/dt = (+/-) sqrt(2GM/rc2)(1-Rs/r) = Rs/r Since radius decreases as time increases, the negative root is the correct one: dr/dt = -c sqrt(Rs/r)(1-Rs/r) I calculated that the momentum (not 4-momentum) in this situation should be: p = m v sqrt(1 - Rs/r - v2/(c2(1-Rs/r)) 3. The attempt at a solution When I plug in the velocity into the momentum equation, I get: p = -mc sqrt(Rs/r)(1-Rs/r) / (sqrt(1 - Rs/r - c2(Rs/r)(1 - Rs/r)2/(c2(1-Rs/r))) This reduces to: p = -m c sqrt(Rs/r)(1-Rs/r) / sqrt((1 - Rs/r)(1 - Rs/r)) This reduces to p = -m c sqrt(Rs/r) However, if I change the second last equation to be: p = m c sqrt(Rs/r)(Rs/r-1) / sqrt((Rs/r-1)(Rs/r-1)) This reduces to p = m c sqrt(Rs/r) So depending on how I do my calculations, I can get the answer or the negative of the answer, even when I start out with the correct root.