Three dimensional near-horizon metrics that are Einstein-Weyl

TL;DR

This paper explores three-dimensional near-horizon metrics that support Einstein-Weyl structures, providing explicit examples and linking some solutions to well-known integrable systems like dispersionless KP and Hirota types.

Contribution

It identifies specific near-horizon metrics compatible with Einstein-Weyl structures and connects these solutions to integrable systems such as dispersionless KP and Hirota types.

Findings

Explicit examples of near-horizon Einstein-Weyl metrics

Some solutions relate to dispersionless KP and Hirota structures

Demonstrates compatibility conditions for metrics and 1-forms

Abstract

We investigate which three dimensional near-horizon metrics $g_{NH}$ admit a compatible 1-form $X$ such that $(X, [g_{NH}])$ defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.