Class of colliding plane waves in terms of Jacobi functions

TL;DR

This paper introduces a broad class of noncolinear colliding wave solutions in Einstein-Maxwell theory, expressed via Jacobi functions, with parameters allowing avoidance of typical focusing singularities.

Contribution

It provides a new family of exact solutions using Jacobi functions, expanding the understanding of colliding wave phenomena in Einstein-Maxwell equations.

Findings

Solutions characterized by six free parameters

Parameters can be tuned to avoid focusing singularities

Expressed through Jacobi functions depending on advanced and retarded times

Abstract

We present a general class of noncolinear colliding wave solutions of the Einstein-Maxwell equations given in terms of fourth order polynomials, which in turn can be expressed through Jacobi functions depending on generalized advanced and retarded time coordinates. The solutions are characterized by six free parameters. The parameters can be chosen in such a way to avoid the generic focusing singularity