Solutions of the Ortvay Rudolf International Competition in Physics: Can One See One’s Own Back Around a Black Hole? (1991/12 Problem)

This paper is the fifth in a series of published solutions 1–4 discussing problems of the Ortvay Rudolf international competition. The problem treated below is an exercise in general relativity and geometrical optics. Specifically, we check and interpret an often-heard statement, roughly of the form: “If you were to orbit a black hole around its photon sphere, you would see the back of your own head”. As the calculation involves general relativity, the full treatment of the problem as given in this article is appropriate for university students in advanced classes. However, by omitting the relativistic calculations and only referring to the results, one can easily formulate the problem as an exercise in geometric optics in a way that could be appropriate for introductionary level.