Complex Kerr Geometry and Nonstationary Kerr Solutions

TL;DR

This paper explores the complex structure of Kerr geometry using the Kerr-Schild approach, extending it to nonstationary cases with arbitrary spinning source motion, and introduces solutions involving lightlike radiation.

Contribution

It provides a general exact solution for nonstationary Kerr geometry with arbitrary source motion, extending known solutions to include acceleration and radiation effects.

Findings

Derived a nonstationary Kerr solution with arbitrary spinning source motion.

Showed acceleration leads to lightlike radiation along null congruence.

Generalized the 'photon rocket' solutions to rotating Kerr geometries.

Abstract

In the frame of the Kerr-Schild approach, we consider the complex structure of Kerr geometry which is determined by a complex world line of a complex source. The real Kerr geometry is represented as a real slice of this complex structure. The Kerr geometry is generalized to the nonstationary case when the current geometry is determined by a retarded time and is defined by a retarded-time construction via a given complex world line of source. A general exact solution corresponding to arbitrary motion of a spinning source is obtained. The acceleration of the source is accompanied by a lightlike radiation along the principal null congruence. It generalizes to the rotating case the known Kinnersley class of "photon rocket" solutions.