Touching ghosts: observing free fall from an infalling frame of reference into a Schwarzschild black hole

Abstract

The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are introduced to analyse this situation, and the pedagogic value of introducing this alternative coordinate system is demonstrated by their ability to provide a graphically based solution to and illustration of this problem. The counterintuitive result that is obtained, which will be of interest to those studying general relativity at an introductory level at final year undergraduate or at graduate level, is that Bob appears to reach a ghostly image of Alice at the event horizon.