Charge constraint on M87* with twisted light

Abstract

We propose a novel method to constrain the electric charge of the supermassive black hole M87* by analyzing the orbital angular momentum content of the light it emits. By leveraging the established analogy between rotating spacetimes and inhomogeneous optical media, we derive a simple analytical formula that relates the average orbital angular momentum in the observed radiation to the black hole's charge-to-mass ratio. Applying this relation to existing observational data, we place an upper bound of $Q/M\lesssim 0.39$ on the charge of M87*. While the analysis focuses on electric charge, which is used here purely as a theoretical example since astrophysical black holes are expected to be approximately neutral, the method is general and can be extended to constrain other types of charges – degrees of freedom that define distinct black hole solutions. These results demonstrate the potential of orbital angular momentum as a new fundamental degree of freedom to be exploited in astrophysics, providing a complementary and independent alternative to shadow-based techniques for probing the properties of rotating compact objects and testing gravity in the strong-field regime.