Question

Relativistic case: Starting from equation $\frac{dt}{dr} = -(\frac{2M}{r})^{-1/2}(1-\frac{2M}{r})^{-1}$ invert it to get $\frac{dr}{dt}$. Restore factors of G and c. Get the expression for V(r), the "coordinate speed," for a particle falling from rest at $\infty$. Take the Derivative with respect to r to find the location where the maximum coordinate speed occurs.

Answer 1

r- 2m dtdt ldr V(r)--IQM) co-ordinate speed- (1-2m for maximum co-ordinate speed (2)2 ( 1-2m 2 m so co-ordinate speed is maximum at r = 6*M