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Dyonic Kerr-Schild ansatz

Eloy Ayón-Beato1,*, Daniel Flores-Alfonso2,†, Mokhtar Hassaine3,‡, and Daniel F. Higuita-Borja4,5,§

  • *Contact author: eloy.ayon-beato@cinvestav.mx
  • †Contact author: dafa@azc.uam.mx
  • ‡Contact author: hassaine@inst-mat.utalca.cl
  • §Contact author: dfhiguit@gmail.com
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Phys. Rev. D 112, 104020 – Published 10 November, 2025

DOI: https://doi.org/10.1103/l1f2-vxlc

Abstract

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 1-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 1-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 with 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.

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References (34)

  1. R. P. Kerr and A. Schild, in Atti del Convegno sulla Relativita Generale: Problemi dell’Energia e Onde Gravitazionali (G. Barbèra, Firenze, 1965), pp. 1–12.
  2. R. P. Kerr, Phys. Rev. Lett. 11, 237 (1963).
  3. B. Carter, Commun. Math. Phys. 10, 280 (1968).
  4. B. Carter, in Black Holes (Les Houches Lectures), edited by B. S. DeWitt and C. DeWitt (Gordon and Breach, New York, 1972); Gen. Relativ. Gravit. 41, 2873 (2009).
  5. J. F. Plebański, Ann. Phys. (N.Y.) 90, 196 (1975).
  6. E. T. Newman, R. Couch, K. Chinnapared, A. Exton, A. Prakash, and R. Torrence, J. Math. Phys. (N.Y.) 6, 918 (1965).
  7. M. Demiański and E. Newman, Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 14, 653 (1966), https://www.zbmath.org/0184.55102.
  8. E. Ayon-Beato and M. Hassaine, Phys. Rev. D 73, 104001 (2006).
  9. E. Ayón-Beato, D. Higuita-Borja, J. A. Méndez-Zavaleta, and G. Velázquez-Rodríguez, Phys. Rev. D 97, 084045 (2018).
  10. G. C. Debney, R. P. Kerr, and A. Schild, J. Math. Phys. (N.Y.) 10, 1842 (1969).
  11. D. Cox and E. J. Flaherty, Commun. Math. Phys. 47, 75 (1976).
  12. H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge, England, 2003).
  13. E. Ayón-Beato, M. Hassaïne, and D. Higuita-Borja, Phys. Rev. D 94, 064073 (2016).
  14. E. Ayón-Beato, D. Flores-Alfonso, and M. Hassaine, Phys. Rev. D 112, 044059 (2025).
  15. E. Ayón-Beato, D. Higuita-Borja, and J. A. Méndez-Zavaleta, Phys. Rev. D 93, 024049 (2016).
  16. M. Ortaggio and A. Srinivasan, Phys. Rev. D 110, 044035 (2024).
  17. A. Srinivasan, Phys. Rev. D 111, 064061 (2025).
  18. E. Ayón-Beato, D. Flores-Alfonso, and M. Hassaïne, Phys. Rev. D 110, 064027 (2024).
  19. T. Ortín, Gravity and Strings (Cambridge University Press, Cambridge, England, 2004).
  20. B. Carter, Commun. Math. Phys. 17, 233 (1970).
  21. A. Papapetrou, Ann. Inst. H. Poincare Phys. Theor. 4, 83 (1966), https://www.numdam.org/item/AIHPA_1966__4_2_83_0/.
  22. W. Kundt and M. Trumper, Z. Phys. 192, 419 (1966).
  23. B. Carter, J. Math. Phys. (N.Y.) 10, 70 (1969).
  24. M. Heusler, Black Hole Uniqueness Theorems (Cambridge University Press, Cambridge, England, 1996).
  25. R. H. Boyer and R. W. Lindquist, J. Math. Phys. (N.Y.) 8, 265 (1967).
  26. D. Higuita-Borja, The role of symmetries in Kerr’s theorem and its generalizations, Ph.D. thesis, Departamento de Física, Cinvestav, 2018.
  27. G. W. Gibbons, H. Lu, D. N. Page, and C. N. Pope, J. Geom. Phys. 53, 49 (2005).
  28. G. Clement and C. Leygnac, Phys. Rev. D 70, 084018 (2004).
  29. A. A. García-Díaz, arXiv:2112.06302; Ann. Phys. (Amsterdam) 441, 168880 (2022).
  30. E. Ayón-Beato, Ann. Phys. (Amsterdam) 469, 169771 (2024).
  31. I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, Phys. Rev. D 102, 121703 (2020).
  32. J. Barrientos, A. Cisterna, M. Hassaïne, and K. Pallikaris, Phys. Lett. B 860, 139214 (2025).
  33. M. Hassaine, D. Kubiznak, and A. Srinivasan, Phys. Rev. D 111, L061502 (2025).
  34. M. B. Green, N. D. Lambert, G. Papadopoulos, and P. K. Townsend, Phys. Lett. B 384, 86 (1996).

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Phys. Rev. D 112, 104020– Published 10 November, 2025
  • Received 6 August 2025
  • Accepted 13 October 2025
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