Light-Like Boost of the Kerr Gravitational Field

TL;DR

This paper investigates how the Kerr gravitational field transforms under light-like boosts in different directions, revealing impulsive gravitational wave characteristics and confirming previous theoretical results.

Contribution

It provides a detailed analysis of light-like boosts of the Kerr field, emphasizing the Riemann tensor approach to clarify previous diverse findings.

Findings

Boosted field in the transverse case is an impulsive gravitational wave with a shifted line singularity.

Parallel boost results are unaffected by the source's rotation.

The analysis confirms the limits previously calculated by Balasin and Nachbagauer.

Abstract

We describe light-like boosts of the Kerr gravitational field transverse and parallel to the symmetry axis. In the transverse case the boosted field is that of an impulsive gravitational wave having a line singularity displaced relative to its position if the rotation of the source were removed. The parallel boost is insensitive to the rotation of the source. The literature contains a number of diverse results for light-like boosts of the Kerr gravitational field. Our conclusions confirm the correctness of the limits calculated by Balasin and Nachbagauer [Class.and Quantum Grav.13(1996),731]. To avoid any ambiguity our approach is centered on evaluating the light-like boost of the Riemann tensor for the Kerr space-time with the metric playing a secondary role.