Photon regions in stationary axisymmetric spacetimes and umbilic conditions

TL;DR

This paper explores the geometric structure of photon regions in stationary axisymmetric spacetimes, introducing a foliation approach that satisfies umbilic conditions to better understand photon trajectories.

Contribution

It proposes a new geometric framework for photon regions based on foliation into fundamental photon hypersurfaces satisfying umbilic conditions.

Findings

Defines fundamental photon hypersurfaces in stationary spacetimes

Establishes umbilic condition for tangent subbundles

Provides a geometric description of photon regions

Abstract

We present the fundamentals of the recently proposed geometric description of photon regions in terms of foliation into fundamental photon hypersurfaces, which satisfies the umbilic condition for the subbundle of the tangent bundle defined by the generalized impact parameter.