Incommunicado?

In later problems we will encounter the behavior of light near a black hole, particularly its inability to escape from a black hole. That is, if you are trapped inside a black hole and are still alive, you cannot communicate with your friends outside because nothing escapes.

Meanwhile, consider a related problem in a normal space environment. Suppose you and your friend are in separate rocket ships that begin next to each other and accelerate with respect to the stars in opposite directions. You both maintain steady pulsed light communication with each other via intense, non-diverging laser beams. But your relative speed is increasing each second as the separation distance grows ever faster. Will there come a time when neither of you will receive the other’s light beam?

Answer

No and yes! No, in the normal sense case because the relative velocity can never exceed the speed of light. The successive pulses may arrive less and less often, but you will never outrun the light.

And yes, you would lose communication contact if we allow the space itself to expand, analogous to the expansion of the universe in present cosmological models. The addition of velocities is the old classical physics one, not the relativistic one. The photon velocity is affected by the local environment; the local substratum (i.e., coordinate system) “drags” the photon along. Imagine two local regions in rapid recession from each other. If the person in one region fires a photon toward the other, the substratum of the first region drags the photon along, slowing the photon’s progress toward its target. If the expansion rate is high enough, the two regions can be receding from each other at light speed or greater, preventing communication between you and your friend.