Reference-covariant optical holonomy in finite-distance black-hole lensing
Year: 2026
Type: article
Abstract: Finite-distance gravitational deflection in a static, spherically symmetric spacetime is formulated as a framed relative holonomy of the Levi-Civita connection of the equatorial optical manifold. The radial curvature primitive used in Gauss–Bonnet lensing is shown to coincide with the azimuthal component of the optical spin connection. With endpoint-matched polar frames, the total deflection of a ray in winding sector w is the line integral of the physical connection relative to the Euclidean polar connection along the lift of the ray to the universal angular cover. Under the static, spherically symmetric assumptions, the resulting expression is exact, contains no auxiliary closing curve, and applies to multi-winding trajectories. In optical proper-radial coordinates, the metric is determined by a circumference function F ( ρ ), with connection − F ′ ( ρ ) d ϕ and Gaussian curvature − F ″ ( ρ ) / F ( ρ ) . A nondegenerate unstable photon sphere yields the strong-deflection coefficient a ¯ = ( b c − K c ) − 1 . For a degenerate critical orbit, if the first nonzero derivative of the optical curvature is of order p ≥ 1, the singular deflection scales as | b / b c − 1 | − p / [ 2 ( p + 2 ) ] .
Source: Physics Letters B
Authors: Ali Övgün, Reggie C. Pantig
Institutions: Eastern Mediterranean University, Mapúa University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7214895733