New test on the Einstein equivalence principle through the photon ring of black holes

TL;DR

This paper proposes a novel observational method using black hole photon rings to test the Einstein equivalence principle (EEP) in strong gravity regimes, extending previous tests to new scales and polarization effects.

Contribution

It introduces a new approach to test EEP via photon ring size dependence on polarization, incorporating black hole rotation effects and providing analytic expressions for EEP violation constraints.

Findings

Photon ring size depends on polarization in EEP-violating scenarios.

Small EEP violations cause proportional changes in photon ring size.

Black hole rotation has a weak effect on EEP violation constraints.

Abstract

Einstein equivalence principle (EEP), as one of the foundations of general relativity, is a fundamental test of gravity theories. In this paper, we propose a new method to test the EEP of electromagnetic interactions through observations of black hole photon rings, which naturally extends the scale of Newtonian and post-Newtoian gravity where the EEP violation through a variable fine structure constant has been well constrained to that of stronger gravity. We start from a general form of Lagrangian that violates EEP, where a specific EEP violation model could be regarded as one of the cases of this Lagrangian. Within the geometrical optical approximation, we find that the dispersion relation of photons is modified: for photons moving in circular orbit, the dispersion relation simplifies, and behaves such that photons with different linear polarizations perceive different gravitational potentials. This makes the size of black hole photon ring depend on polarization. Further assuming that the EEP violation is small, we derive an approximate analytic expression for spherical black holes showing that the change in size of the photon ring is proportional to the violation parameters. We also discuss several cases of this analytic expression for specific models. Finally, we explore the effects of black hole rotation and derive a modified proportionality relation between the change in size of photon ring and the violation parameters. The numerical and analytic results show that the influence of black hole rotation on the constraints of EEP violation is relatively weak for small magnitude of EEP violation and small rotation speed of black holes.