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Non-relativistic twistor theory and Newton-Cartan geometry

dc.creatorDunajski, Maciej Lukasz
dc.creatorGundry, James
dc.description.abstractWe develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O ⊕ O(2). We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.
dc.publisherCommunications in Mathematical Physics
dc.rightsAttribution 2.0 UK: England & Wales
dc.titleNon-relativistic twistor theory and Newton-Cartan geometry

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