Is it possible to distinguish between different black hole solutions using the Shapiro time delay?

Abstract

In this paper we propose to use Shapiro time delay as a tool to distinguish between different black hole solutions. We calculate the analytic Shapiro time, using first-order expansions, for four solutions. They are Schwarzschild, Reissner-Nordstr\"o{}m, Bardeen, and Ay\'on-Beato and Garc\'ia. We created a numerical experiment, based on measurements made in the solar system, consisting of the round trip path of light passing through a black hole at the center. We obtained different delay times varying between the order of $10^{-4}$s and $10^{-6}$s, for a stellar black hole; and variations of the order of hours, for a supermassive one. Considering that the accuracy currently achieved in measurements made in the solar system are on the order of $10^{-12}$s, we believe that this mechanism could be used in black hole model determination in the near future.