Three dimensional near-horizon metrics that are Einstein-Weyl
Abstract
We investigate which three dimensional near-horizon metrics gNH admit a compatible 1-form X such that (X, [gNH]) 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.
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