Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
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| Format: | Preprint |
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2024
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| author | Cardoso, Gabriel Lopes Mahapatra, Swapna Nagy, Silvia |
| author_facet | Cardoso, Gabriel Lopes Mahapatra, Swapna Nagy, Silvia |
| contents | We consider the dimensional reduction to two dimensions of certain gravitational theories in $D \geq 4$ dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl-Lewis-Papapetrou coordinates. In contrast with previous proposals, we find that the gauge group of the Yang-Mills single copy carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, the Kaluza-Klein rotating attractor solution, the Einstein-Rosen wave solution and the self-dual Kleinian Taub-NUT solution. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_14392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy Cardoso, Gabriel Lopes Mahapatra, Swapna Nagy, Silvia High Energy Physics - Theory General Relativity and Quantum Cosmology We consider the dimensional reduction to two dimensions of certain gravitational theories in $D \geq 4$ dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl-Lewis-Papapetrou coordinates. In contrast with previous proposals, we find that the gauge group of the Yang-Mills single copy carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, the Kaluza-Klein rotating attractor solution, the Einstein-Rosen wave solution and the self-dual Kleinian Taub-NUT solution. |
| title | Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2407.14392 |