Abstract
Freudenthal duality (FD) is a non-linear symmetry of the Bekenstein-Hawking entropy of extremal dyonic black holes (BHs) in Maxwell-Einstein-scalar theories in four space-time dimensions realized as an anti-involutive map in the symplectic space of electric-magnetic BH charges. In this paper, we generalize FD to the class of rotating (stationary) extremal BHs, both in the under- and over-rotating regime, defining a (generalized) rotating FD (generally, non-anti-involutive) map (RFD), which also acts on the BH angular momentum. We prove that the RFD map is unique, and we compute the explicit expression of its non-linear action on the angular momentum itself. Interestingly, in the non-rotating limit, RFD bifurcates into the usual, non-rotating FD branch and into a spurious branch, named “golden” branch, mapping a non-rotating (static) extremal BH to an under-rotating (stationary) extremal BH, in which the ratio between the angular momentum and the non-rotating entropy is the square root of the golden ratio. Finally, we investigate the possibility of inducing transitions between the under- and over- rotating regimes by means of RFD, obtaining a no-go result.
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Acknowledgments
The work of AC is supported by the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement number 101034383. The work of TM is supported by the grant SB/SJF/2019-20/08. The work of AM is supported by a “Maria Zambrano” distinguished researcher fellowship at the University of Murcia, Spain, financed by the European Union within the NextGenerationEU programme.
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Chattopadhyay, A., Mandal, T. & Marrani, A. Generalized Freudenthal duality for rotating extremal black holes. J. High Energ. Phys. 2024, 170 (2024). https://doi.org/10.1007/JHEP03(2024)170
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DOI: https://doi.org/10.1007/JHEP03(2024)170