General Relativity: An Introduction for Physicists · Problem 1.16
The spacetime of special relativity — Hobson, Efstathiou & Lasenby
Physics · uniform-acceleration-event-horizon
Problem
If the spaceship in Exercise 1.15 left base at time t=τ=0 and travelled forever in a straight line with constant acceleration f, show that no signal sent by base later than time t=c/f can ever reach the spaceship. By sketching an appropriate spacetime diagram show that light signals sent from the base appear increasingly redshifted to an observer on the spaceship. If the acceleration of the spaceship is g (for the comfort of its occupants), how long by the spaceship clock does it take to reach a star 10 light years from the base?