Charge constraint on M87* with twisted light

TL;DR

This paper introduces a new method to constrain the electric charge of the black hole M87* by analyzing the orbital angular momentum of emitted light, offering an alternative to shadow-based techniques.

Contribution

The authors derive an analytical formula linking orbital angular momentum of light to black hole charge and apply it to observational data to set an upper bound on M87*'s charge-to-mass ratio.

Findings

Upper bound of $oxed{ ext{Q}/ ext{M} \, \lesssim \, 0.39}$ on M87*'s charge.

Method demonstrates orbital angular momentum as a new probe for black hole properties.

Provides an independent technique for testing gravity in strong-field regimes.

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 $\mathcal{Q}/M \lesssim 0.39$ 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 $\unicode{x2013}$ 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.