General Relativity: An Introduction for Physicists · Problem 9.23
The Schwarzschild geometry — Hobson, Efstathiou & Lasenby
Physics · redshift-from-infalling-particle
Problem
An observer at rest at coordinate radius r=R in the Schwarzschild geometry drops a massive particle which free-falls radially inwards. When the particle is at a coordinate radius r=rE it emits a photon radially outwards. Find an expression for the redshift z of the photon when it is received by the observer. Show that z→∞ as rE→2GM/c2.