Non-Analytic Extension of the Kinnersley-Chitre Group for Colliding Plane Gravitational Waves. I

TL;DR

This paper develops a method to extend the Kinnersley-Chitre group for colliding plane gravitational waves using a homogeneous Hilbert problem formalism, specifically applied to the collinear polarization case.

Contribution

It introduces a non-analytic extension of the Kinnersley-Chitre group for solutions of the hyperbolic Ernst equation in colliding gravitational waves, advancing the mathematical framework.

Findings

Constructed the extension for collinear polarization case.

Applied homogeneous Hilbert problem formalism.

Provided a foundation for further generalizations.

Abstract

A program is outlined concerning the set of all solutions of the hyperbolic Ernst equation on a two-dimensional manifold whose underlying topological space is the same as the domain of all Ernst potentials for colliding plane gravitational wave pairs. The aim of the program is to construct and apply a non-trivial extension of the group of Kinnersley-Chitre transformations. This is to be done by employing the formalism of a homogeneous Hilbert problem. In this first paper of a series, the aforementioned program is completely carried out for the collinear polarization case.