Proof of a generalized Geroch conjecture for the hyperbolic Ernst equation

TL;DR

This paper generalizes Geroch's conjecture to include non-analytic solutions of the hyperbolic Ernst equation, expanding the understanding of solution behaviors beyond the analytic case.

Contribution

It proves a generalized version of Geroch's conjecture applicable to non-analytic solutions of the hyperbolic Ernst equation, broadening the scope of the original conjecture.

Findings

Proof of the generalized Geroch conjecture for hyperbolic Ernst solutions

Extension of the conjecture to non-analytic solutions

Applicability to solutions not accessible along the axis

Abstract

We enunciate and prove here a generalization of Geroch's famous conjecture concerning analytic solutions of the elliptic Ernst equation. Our generalization is stated for solutions of the hyperbolic Ernst equation that are not necessarily analytic, although it can be formulated also for solutions of the elliptic Ernst equation that are nowhere axis-accessible.