Kerr-Schild Approach to the Boosted Kerr Solution

TL;DR

This paper presents an exact analysis of boosted Kerr geometries using complex methods, revealing new light-like solutions with angular momentum in ultrarelativistic limits and detailed geometric properties.

Contribution

It provides explicit formulas for boosted Kerr metrics and null congruences, extending previous solutions to arbitrary boosts and orientations with novel ultrarelativistic results.

Findings

Derived explicit metrics and null congruences for boosted Kerr solutions.

Obtained light-like solutions with non-zero angular momentum in ultrarelativistic limit.

Discussed implications for related fields and theoretical models.

Abstract

Using a complex representation of the Debney-Kerr-Schild (DKS) solutions and the Kerr theorem we analyze the boosted Kerr geometries and give the exact and explicit expressions for the metrics, the principal null congruences, the coordinate systems and the location of the singularities for arbitrary value and orientation of the boost with respect to the angular momentum. In the limiting, ultrarelativistic case we obtain light-like solutions possessing diverging and twisting principal null congruences and having, contrary to the known pp-wave limiting solutions, a non-zero value of the total angular momentum. The implications of the above results in various related fields are discussed.