- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

New Asymptotically Flat Einstein-Maxwell Instantons

Bernardo Araneda1,2,* and Maciej Dunajski3,4,†

  • *Contact author: baraneda@ed.ac.uk, bernardo.araneda@aei.mpg.de
  • †Contact author: m.dunajski@damtp.cam.ac.uk
PDF

Phys. Rev. Lett. 135, 241501 – Published 9 December, 2025

DOI: https://doi.org/10.1103/f3ls-znl6

Abstract

We disprove the Euclidean Einstein-Maxwell black hole uniqueness conjecture, and thus demonstrate that the semiclassical properties of coupled gravitational and electromagnetic fields are more subtle than expected from Lorentzian general relativity, where the Kerr-Newman family of metrics yields the most general stationary and asymptotically flat black holes with a single event horizon. This is achieved by an explicit construction of a new three-parameter family of asymptotically flat Einstein-Maxwell instantons. These solutions are toric, regular, and free of conical and orbifold singularities on the manifold M=CP2\S1. In the case of vanishing charge, these instantons reduce to the Chen-Teo Ricci-flat instantons.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (26)

  1. S. W. Hawking, Gravitational instantons, Phys. Lett. 60A, 81 (1977).
  2. M. Dunajski, Gravitational instantons, old and new, Acta Phys. Pol. B 55, 12-A3 (2024).
  3. G. W. Gibbons and S. W. Hawking, Euclidean Quantum Gravity, (World Scientific, Singapore, 1993).
  4. G. W. Gibbons and S. W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D 15, 2752 (1977).
  5. P. T. Chruściel, J. Lopes Costa, and M. Heusler, Stationary black holes: Uniqueness and beyond, Living Rev. Relativity 15, 7 (2012).
  6. A. S. Lapedes, Black hole uniqueness theorems in Euclidean quantum gravity, Phys. Rev. D 22, 1837 (1980).
  7. Y. Chen and E. Teo, A new AF gravitational instanton, Phys. Lett. B 703, 359 (2011).
  8. A. R. Brown, L. V. Iliesiu, G. Penington, and M. Usatyuk, The evaporation of charged black holes, arXiv:2411.03447.
  9. P. T. Chruściel, H. S. Reall, and P. Tod, On Israel-Wilson-Perjés black holes, Classical Quantum Gravity 23, 2519 (2006).
  10. M. Dunajski and S. A. Hartnoll, Einstein-Maxwell gravitational instantons and five dimensional solitonic strings, Classical Quantum Gravity 24, 1841 (2007).
  11. Y. Chen and E. Teo, Five-parameter class of solutions to the vacuum Einstein equations, Phys. Rev. D 91, 124005 (2015).
  12. P. Tod, One-sided type-D metrics with aligned Einstein- Maxwell, arXiv:2410.13410.
  13. S.-T. Yau, in Problem Section, edited by S.-T. Yau, Seminar on Differential Geometry, volume 102 of Annals of Mathematics Studies (Princeton University Press, 1982), pp. 669–706.
  14. B. Araneda, Hidden symmetries of generalised gravitational instantons, Ann. Henri Poincaré, 26, 4021 (2025).
  15. N. M. J. Woodhouse and L. J. Mason, The Geroch group and non Hausdorff twistor spaces, Nonlinearity 1, 73 (1988).
  16. B. Araneda and M. Dunajski, Toric Einstein-Maxwell gravitational instantons (to be published).
  17. Y. Chen and E. Teo, Rod-structure classification of gravitational instantons with U(1)×U(1) isometry, Nucl. Phys. B838, 207 (2010).
  18. T. Harmark, Stationary and axisymmetric solutions of higher-dimensional general relativity, Phys. Rev. D 70, 124002 (2004).
  19. H. K. Kunduri and J. Lucietti, Existence and uniqueness of asymptotically flat toric gravitational instantons, Lett. Math. Phys. 111, 133 (2021).
  20. P. Tod, Rod structures and patching matrices: A review, arXiv:2411.02096.
  21. G. W. Gibbons and S. W. Hawking, Classification of gravitational instanton symmetries, Commun. Math. Phys. 66, 291 (1979).
  22. S. Aksteiner and L. Andersson, Gravitational instantons and special geometry, J. Diff. Geom. 128, 928 (2024).
  23. O. Biquard and P. Gauduchon, On toric Hermitian ALF gravitational instantons, Commun. Math. Phys. 399, 389 (2023).
  24. M. Dunajski and P. Tod, Twistor theory of the Chen–Teo gravitational instanton, Classical Quantum Gravity 41, 195008 (2024).
  25. M. Li and S. Sun, Gravitational instantons and harmonic maps, arXiv:2507.15284.
  26. M. Dunajski, Solitons, Instantons, and Twistors, 2nd ed., Oxford Graduate Texts in Mathematics Vol. 31 (Oxford University Press, New York, 2024).

Outline

Information

Phys. Rev. Lett. 135, 241501– Published 9 December, 2025
  • Received 10 October 2025
  • Accepted 17 November 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation