Abstract
We show that the classical double copy relationship for Kerr-Schild spacetimes can be dimensionally reduced to give a natural notion of the double copy for Kaluza-Klein theory with gravity coupled to a gauge field and a dilaton. Under dimensional reduction the Kerr-Schild (KS) ansatz becomes the stringy Kerr-Schild (sKS) ansatz introduced by Wu. This ansatz captures many Kaluza-Klein black hole solutions, including single-charge black holes arising in both gauged and ungauged supergravity theories. We identify the single copy gauge field and scalar field of an arbitrary sKS solution. We show that the boost-reduction procedure for generating charged black hole solutions can be generalized to any stationary KS seed, and used to combine the metric with the zeroth and single copies of that seed into a single sKS solution. Furthermore, we comment on multi-charge solutions that can be written in a multi-sKS form, proposing a double copy interpretation involving multiple single copy sectors.
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Acknowledgments
We thank Ibrahima Bah and Pierre Heidmann for useful conversations and feedback regarding this work, as well as Chris White and Rodolfo Russo for discussions following the first version of the paper. The work of PW is supported in part by NSF grant PHY-2112699, and RD is supported by an NSF Graduate Research Fellowship.
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Dempsey, R., Weck, P. Compactifying the Kerr-Schild double copy. J. High Energ. Phys. 2023, 198 (2023). https://doi.org/10.1007/JHEP05(2023)198
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DOI: https://doi.org/10.1007/JHEP05(2023)198