The dyonic Kerr-Schild ansatz
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918192760225792 |
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| author | Ayón-Beato, Eloy Flores-Alfonso, Daniel Hassaine, Mokhtar Higuita-Borja, Daniel F. |
| author_facet | Ayón-Beato, Eloy Flores-Alfonso, Daniel Hassaine, Mokhtar Higuita-Borja, Daniel F. |
| contents | We develop a geometric extension of the Kerr-Schild ansatz that incorporates both electric and magnetic sectors of the Maxwell field in a unified framework, without resorting to duality rotations. We start observing that the known purely electric solution satisfies Maxwell's equations due to a closedness condition obeyed by the Kerr-Schild null congruence. From the associated local exactness property, we construct a new one-form naturally linked to the congruence as a sort of Poincaré dualization. This leads us to propose a geometrically motivated dyonic vector potential within the Kerr-Schild ansatz, defined as a superposition of an electric contribution along the congruence and a magnetic one that aligns to the dualized one-form. We then show that for a stationary and axisymmetric Kerr-Schild ansatz, the electrovac circularity theorem uniquely constrains not only the scalar profile of the metric, but also those associated to the electric-magnetic splitting of the gauge field. The resulting formalism provides a transparent derivation of the dyonic Kerr-Newman solution and extends naturally to the (A)dS case, highlighting the intrinsic interplay between geometry and matter in a Kerr-Schild setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02986 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The dyonic Kerr-Schild ansatz Ayón-Beato, Eloy Flores-Alfonso, Daniel Hassaine, Mokhtar Higuita-Borja, Daniel F. High Energy Physics - Theory General Relativity and Quantum Cosmology We develop a geometric extension of the Kerr-Schild ansatz that incorporates both electric and magnetic sectors of the Maxwell field in a unified framework, without resorting to duality rotations. We start observing that the known purely electric solution satisfies Maxwell's equations due to a closedness condition obeyed by the Kerr-Schild null congruence. From the associated local exactness property, we construct a new one-form naturally linked to the congruence as a sort of Poincaré dualization. This leads us to propose a geometrically motivated dyonic vector potential within the Kerr-Schild ansatz, defined as a superposition of an electric contribution along the congruence and a magnetic one that aligns to the dualized one-form. We then show that for a stationary and axisymmetric Kerr-Schild ansatz, the electrovac circularity theorem uniquely constrains not only the scalar profile of the metric, but also those associated to the electric-magnetic splitting of the gauge field. The resulting formalism provides a transparent derivation of the dyonic Kerr-Newman solution and extends naturally to the (A)dS case, highlighting the intrinsic interplay between geometry and matter in a Kerr-Schild setting. |
| title | The dyonic Kerr-Schild ansatz |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.02986 |