Twistor space origins of the Newman-Penrose map

Journal Article · Mon Oct 24 00:00:00 EDT 2022 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.13.4.099· OSTI ID:1894384

Farnsworth, Kara ^[1]; Graesser, Michael L. ^[2]; Herczeg, Gabriel ^[3]

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1. Case Western Reserve University
2. Los Alamos National Laboratory
3. Brown University

Recently, we introduced the “Newman-Penrose map”, a novel correspondence between a certain class of solutions of Einstein’s equations and self-dual solutions of the vacuum Maxwell equations, which we showed was closely related to the classical double copy. Here, we give an alternative definition of this correspondence in terms of quantities that are defined naturally on twistor space, and a shear-free null geodesic congruence on Minkowski space whose twistorial character is articulated by the Kerr theorem. The advantage of this reformulation is that it is purely geometrical in nature, being manifestly invariant under both spacetime diffeomorphisms and projective transformations on twistor space. While the original formulation of the map may be more convenient for most explicit calculations, the twistorial formulation we present here may be of greater theoretical utility.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: Simons Foundation; USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC). High Energy Physics (HEP)
• Grant/Contract Number: 89233218CNA000001; AC52-06NA25396
• OSTI ID: 1894384
• Alternate ID(s): OSTI ID: 1972108
• Report Number(s): LA-UR-21-23751; 099
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 4 Vol. 13; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English

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