Deflection Angle in the Strong Deflection Limit and Quasinormal Modes in Stationary Axisymmetric Spacetimes

TL;DR

This paper establishes a coordinate-invariant formula for photon deflection angles in strong gravitational fields of rotating spacetimes and links these lensing effects to quasinormal modes through curvature-dependent coefficients.

Contribution

It introduces a curvature-based, model-independent relation between strong deflection lensing and quasinormal modes in stationary axisymmetric spacetimes.

Findings

Derived a coordinate-invariant deflection angle formula in SDL.

Linked the logarithmic divergence coefficient to local curvature quantities.

Connected quasinormal mode damping rates to lensing characteristics.

Abstract

We derive a coordinate-invariant expression for the photon deflection angle in the strong deflection limit (SDL) of stationary axisymmetric spacetimes. The key logarithmic-divergence coefficient is shown to depend only on quantities locally measurable by a zero-angular-momentum observer -- curvature scalars, the circumferential radius, and the proper angular velocity. The same coefficient governs the damping rate of quasinormal modes (QNMs) in the eikonal limit, establishing a curvature-based, model-independent connection between QNMs and lensing in the SDL near rotating compact objects.