Through the Black Hole -- On Not Breaking Time Reversal Symmetry

Abstract

It is well-known that a particle falling into a black hole will definitely reach the center in finite proper time if it enters the sphere of radius $3r_{s}/2$ where $r_{s}$ is the Schwarzschild radius. It is usually assumed that once the particle reaches the central singularity, it stops. Here it shall be shown that there are no theoretical reasons for this assumption. In fact, due to the time-reversal symmetry of the equation of motion, it is more ``natural'' to assume that the particle will travel through the singularity and come out on the other side. Of course, it is not possible to compute the trajectory of the particle at the singularity itself. However, one may compute the trajectory just before entry and just after exit. The continuity of the two pieces at the singularity is maintained through energy and angular momentum conservation conditions. The results of such computations are shown here. Also, for the particle to come to a stop at the center, there must exist nonconservative forces at that point. Such forces being unknown both theoretically and experimentally, it is prudent to disregard them.