Deflection angle of light near Dunkl-type black holes

Determine the gravitational deflection angle of light near rotating and charged black holes in Dunkl-deformed spacetime, described by the Newman–Janis–generated Boyer–Lindquist metric with rotation parameter a, charge Q, and Dunkl deformation parameters ζ and δ, in order to supplement and complement the shadow-based optical analysis presented for these solutions.

Background

The paper constructs and analyzes non-rotating and rotating charged black hole solutions in Dunkl-deformed spacetime, derives their metric functions via Einstein–Maxwell equations with Dunkl derivatives, and studies shadow properties using the Hamilton–Jacobi formalism together with CUDA-accelerated numerics. Constraints on Dunkl parameters are obtained by comparing the predicted shadow radius with EHT observations.

While the shadow analysis provides key optical observables, the authors explicitly point out that the complementary observable of light deflection (gravitational lensing) near these Dunkl-type black holes has not been addressed and remains an open question. Establishing the deflection angle would enable a more complete optical characterization and strengthen comparisons with observational data.