General Relativity: An Introduction for Physicists · Problem 9.12
The Schwarzschild geometry — Hobson, Efstathiou & Lasenby
Physics · radial-infall-from-rest
Problem
A particle is dropped from rest at a coordinate radius r=R in the Schwarzschild geometry. Obtain an expression for the 4-velocity of the particle in (t,r,θ,ϕ) coordinates when it passes coordinate radius r.