A Covariant Construction of Maslov Phases in Strong-Field Kerr Null Optics

A covariant construction of the caustic, or Maslov, phase in strong-field null optics is formulated. The transverse dynamics of a narrow bundle are encoded on a parallel-transported Sachs screen by the optical tidal matrix, defined via the projection of the Riemann tensor onto the Sachs basis, and propagated by the Jacobi equation. For each null branch connecting fixed endpoints, the Morse-Maslov index is defined by the number of conjugate-point crossings encountered along the trajectory. By utilizing the Jacobi-Van Vleck-Morette relation and the WKB approximation of the frequency-domain Green function, it is shown that each branch contribution carries a universal phase factor determined by this index. An operational algorithm for extracting the Maslov index from the evolution of the Jacobi map is presented. Finally, a finite-radius Kerr boundary-value configuration, consisting of a circular equatorial emitter and a static receiver, is established as a benchmark strong-field setup to define endpoint data and conventions. Numerical evaluation of the indices for specific Kerr branches is deferred to future work This manuscript was originally submitted to preprints.org but was not published there. The branding in the PDF is for archival reference only.