Twistor space origins of the Newman-Penrose map
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...
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| Format: | Article |
| Language: | English |
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SciPost
2022-10-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.13.4.099 |
| _version_ | 1797990802849267712 |
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| author | Kara Farnsworth, Michael L. Graesser, Gabriel Herczeg |
| author_facet | Kara Farnsworth, Michael L. Graesser, Gabriel Herczeg |
| author_sort | Kara Farnsworth, Michael L. Graesser, Gabriel Herczeg |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T08:42:01Z |
| format | Article |
| id | doaj.art-65d8ec9a558b40a985f3eaaf3097e01a |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-04-11T08:42:01Z |
| publishDate | 2022-10-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-65d8ec9a558b40a985f3eaaf3097e01a2022-12-22T04:34:10ZengSciPostSciPost Physics2542-46532022-10-0113409910.21468/SciPostPhys.13.4.099Twistor space origins of the Newman-Penrose mapKara Farnsworth, Michael L. Graesser, Gabriel HerczegRecently, 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.https://scipost.org/SciPostPhys.13.4.099 |
| spellingShingle | Kara Farnsworth, Michael L. Graesser, Gabriel Herczeg Twistor space origins of the Newman-Penrose map SciPost Physics |
| title | Twistor space origins of the Newman-Penrose map |
| title_full | Twistor space origins of the Newman-Penrose map |
| title_fullStr | Twistor space origins of the Newman-Penrose map |
| title_full_unstemmed | Twistor space origins of the Newman-Penrose map |
| title_short | Twistor space origins of the Newman-Penrose map |
| title_sort | twistor space origins of the newman penrose map |
| url | https://scipost.org/SciPostPhys.13.4.099 |
| work_keys_str_mv | AT karafarnsworthmichaellgraessergabrielherczeg twistorspaceoriginsofthenewmanpenrosemap |