Complex Structure of Kerr Geometry and Rotating `Photon Rocket' Solutions

TL;DR

This paper generalizes the Kerr solution to a nonstationary, rotating source with arbitrary acceleration, using a complex retarded-time approach, leading to new rotating 'photon rocket' solutions with radiation and complex worldline parameters.

Contribution

It introduces a nonstationary, rotating Kerr-like solution with arbitrary acceleration using a complex retarded-time construction, extending known photon rocket solutions.

Findings

Solutions exhibit geodesic, shear-free principal null congruence.

Acceleration induces lightlike radiation along null congruence.

Generalizes Kinnersley photon rocket solutions to rotating case.

Abstract

In the frame of the Kerr-Schild approach, we obtain a generalization of the Kerr solution to a nonstationary case corresponding to a rotating source moving with arbitrary acceleration. Similar to the Kerr solution, the solutions obtained have the geodesic and shear free principal null congruence. The current parameters of the solutions are determined by a complex retarded-time construction via a given complex worldline of source. The real part of the complex worldline defines the values of the boost and acceleration while the imaginary part controls the rotation. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. The solutions obtained generalize to the rotating case the known Kinnersley class of the "photon rocket" solutions.