Three dimensional near-horizon metrics that are Einstein-Weyl

Matthew Randall

Address: Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

E-mail: randallm@math.muni.cz

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.

AMSclassification: primary 53B15; secondary 53B30, 83C57.

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DOI: 10.5817/AM2017-5-335