Principal equatorial null geodesic congruences in the Kerr metric, and their quantum propagators

Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity; however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.