Shadows in conformally related gravity theories

Abstract

Null geodesics are invariant under a conformal transformation, and thus it might seem natural to assume that the observables corresponding to the shadow of a space-time are also conformally invariant. Here, we argue instead, that since the Arnowitt-Deser-Misner mass and the active gravitational mass of an asymptotically flat space-time are not, in general, invariant under such conformal transformations, the shadow radius for photon motion in a space-time would be quantitatively different, when viewed from two different conformally related frames, although the expression for the shadow radius is similar. We then use this fact to propose a novel method to constrain the relevant parameters in a gravity theory conformally related to general relativity. As examples of our method, we constrain the parameter space in Brans-Dicke theory, and a class of brane-world gravity models, by using the recent observational data of M$87^{*}$ by the Event Horizon Telescope.