Restricted Class of Colliding Einstein-Yang-Mills Plane Waves

TL;DR

This paper constructs a specific class of colliding Einstein-Yang-Mills plane waves by transforming Abelian electromagnetic solutions, revealing connections to known black hole solutions and classical shock wave models.

Contribution

It introduces a new class of colliding EYM plane wave solutions derived from Abelian solutions, extending the understanding of non-Abelian gauge fields in gravitational wave collisions.

Findings

Solution is isometric to Wu-Yang charged Kerr-Newman black hole

Reduces to Bell-Szekeres solution in the linear polarization limit

Shares properties with colliding Einstein-Maxwell plane waves

Abstract

By gauging an Abelian electromagnetic (em) solution through a non-Abelian transformation and in accordance with a theorem proved long time ago, we construct a simple class of colliding Einstein-Yang-Mills (EYM) plane waves. The solution is isometric to the Wu-Yang charged Kerr-Newman (KN) black hole and shares much of the properties satisfied by colliding Einstein-Maxwell (EM) plane waves. In the linear polarization limit with unit degenerate charge it reduces to the Bell-Szekeres (BS) solution for colliding em shock waves.