Curvature without metric: the Penrose construction for half-flat pp-waves

TL;DR

This paper extends the Penrose construction to half-flat pp-waves, deriving the associated data and expressing the Weyl spinor for these plane wave solutions without relying on a metric.

Contribution

It introduces a novel approach to describe half-flat pp-waves using Penrose data, generalizing the original construction for plane waves.

Findings

Derived Penrose data for half-flat pp-waves

Extended Penrose construction to Weyl spinor

Provided a metric-independent description of plane waves

Abstract

We derive the Penrose data for half-flat pp-waves and extend his original construction for the Weyl spinor of plane waves in terms of this data.