Nonstationary Kerr Congruences

TL;DR

This paper generalizes the Kerr null congruence to nonstationary cases, deriving shear-free geodesic null congruences from complex world lines and analyzing related Einstein solutions, including radiative and accelerating cases.

Contribution

It introduces a nonstationary shear-free null congruence generated by complex world lines, extending Kerr solutions to dynamic, radiative, and accelerating scenarios.

Findings

Existence of a complex radiative solution generalizing Kerr

Derivation of nonstationary shear-free geodesic null congruences

Analysis of Einstein equations for dynamic Kerr-like spacetimes

Abstract

The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for nonstationary case is obtained. We find a nonstationary shear free geodesic null congruence which is generated by a given analytical complex world line. Solutions of the Einstein equations are analyzed. It is shown that there exists complex radiative solution which is generalization of the Kerr solution and the Kinnersley accelerating solution for "photon rocket".