Let's say we have a particle free-falling directly towards the center of a black hole. Initially it's at rest at distance r from the center, that is equal to double the Schwarzschild radius of this black-hole. It is followed by a photon that is initially at a distance d behind the particle.
This photon was initially at such distance that it will catch up with this particle exactly when the particle passes the event horizon of this black hole.
How to calculate the initial distance d?
