A note on the Hyper--CR equation, and gauged $N=2$ supergravity

TL;DR

This paper introduces new solutions to the hyper-CR equation and demonstrates how these solutions can generate supersymmetric Einstein-Maxwell cosmological spacetimes in four dimensions.

Contribution

It constructs a new class of solutions to the dispersionless hyper-CR equation and links these solutions to supersymmetric Einstein-Maxwell spacetimes.

Findings

New solutions to the hyper-CR equation are constructed.

Any solution to the hyper-CR equation yields a supersymmetric Einstein-Maxwell spacetime.

The work bridges integrable systems and supergravity solutions.

Abstract

We construct a new class of solutions to the dispersionless hyper--CR equation, and show how any solution to this equation gives rise to a supersymmetric Einstein--Maxwell cosmological space--time in $(3+1)$--dimensions.