A nonstationary generalization of the Kerr congruence

TL;DR

This paper introduces a dynamic, axisymmetric generalization of the Kerr congruence using shear-free null congruences and complex space-time representations, modeling a singular ring that contracts and expands, potentially describing black hole formation.

Contribution

It presents a novel time-dependent Kerr congruence generalization based on the Kerr theorem and complex space-time methods, linking electromagnetic fields and singularities.

Findings

Describes a contracting and expanding singular ring structure.

Associates electromagnetic and eikonal fields with the congruence.

Proposes a model for transition between naked singularity and black hole.

Abstract

Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a singular ring uniformly contracting to a point and expanding then to infinity. Electromagnetic and complex eikonal field distributions are naturally associated with the obtained congruence, with electric charge being necesssarily unit (``elementary''). We conjecture that the corresponding solution to the Einstein-Maxwell equations could describe the process of continious transition of the naked ringlike singularitiy into a rotating black hole and vice versa, under a particular current radius of the singular ring.