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

Abstract

In this paper we propose to use the 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. These are Schwarzschild, Reissner–Nordström, Bardeen, and Ayón-Beato and García. We created a numerical experiment based on measurements in the solar system consisting of the outward and return paths of light traversing a black hole at the center. We obtained different delay times on the order of $$10^{-4}~\hbox {s}$$ 10 - 4 s and $$10^{-6}~\hbox {s}$$ 10 - 6 s for a stellar black hole; and variations on the order of hours for a supermassive hole. Considering that the accuracies currently achieved in solar system measurements are on the order of $$10^{-12}~\hbox {s}$$ 10 - 12 s , we believe that this mechanism could be used in the determination of black hole models in the near future.