Is the event horizon of a black hole physical?

Let me describe a Rindler horizon scenario. Two ships are accelerating together at 1 g for a long time approaching near c. One of them runs out of fuel and stops accelerating. The accelerating ship will see the out of fuel ship fall a little behind, but then become red shifted, clocks on it appear to slow down and asymptotically stop; red shift grows to infinity. The empty ship becomes invisible. The empty ship is never seen to be farther than a short distance away from accelerating ship, as long as it can be seen at all. It is 'trapped' on the Rindler horizon. Of course, for the empty ship, nothing strange has happened. The other ship accelerates away from it, getting ever further away. The empty ship can receive signals from the accelerating one, but any signals it sends can never reach the accelerating ship (because the accelerating ship stays ahead of the light; no contradiction because it had a head start and keeps accelerating.