Generalized Freudenthal duality for rotating extremal black holes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866911827121668096 |
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| author | Chattopadhyay, Arghya Mandal, Taniya Marrani, Alessio |
| author_facet | Chattopadhyay, Arghya Mandal, Taniya Marrani, Alessio |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_10767 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Freudenthal duality for rotating extremal black holes Chattopadhyay, Arghya Mandal, Taniya Marrani, Alessio High Energy Physics - Theory 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. |
| title | Generalized Freudenthal duality for rotating extremal black holes |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.10767 |