Isometries and the double copy
Abstract In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell’s equations. However, it is well known that the vacuum Einstein equ...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2023)162 |
| _version_ | 1797371204964712448 |
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| author | Damien A. Easson Gabriel Herczeg Tucker Manton Max Pezzelle |
| author_facet | Damien A. Easson Gabriel Herczeg Tucker Manton Max Pezzelle |
| author_sort | Damien A. Easson |
| collection | DOAJ |
| description | Abstract In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell’s equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforward example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution. |
| first_indexed | 2024-03-08T18:15:28Z |
| format | Article |
| id | doaj.art-528db995d29048cdad180132773d9d60 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:15:28Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-528db995d29048cdad180132773d9d602023-12-31T12:08:44ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023913110.1007/JHEP09(2023)162Isometries and the double copyDamien A. Easson0Gabriel Herczeg1Tucker Manton2Max Pezzelle3Department of Physics, Arizona State UniversityBrown Theoretical Physics Center, Department of Physics, Brown UniversityBrown Theoretical Physics Center, Department of Physics, Brown UniversityDepartment of Physics, Arizona State UniversityAbstract In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell’s equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforward example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution.https://doi.org/10.1007/JHEP09(2023)162Black HolesGauge-Gravity CorrespondenceSpace-Time Symmetries |
| spellingShingle | Damien A. Easson Gabriel Herczeg Tucker Manton Max Pezzelle Isometries and the double copy Journal of High Energy Physics Black Holes Gauge-Gravity Correspondence Space-Time Symmetries |
| title | Isometries and the double copy |
| title_full | Isometries and the double copy |
| title_fullStr | Isometries and the double copy |
| title_full_unstemmed | Isometries and the double copy |
| title_short | Isometries and the double copy |
| title_sort | isometries and the double copy |
| topic | Black Holes Gauge-Gravity Correspondence Space-Time Symmetries |
| url | https://doi.org/10.1007/JHEP09(2023)162 |
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