All separable supersymmetric AdS5 black holes

James Lucietti (School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK) ; Praxitelis Ntokos (School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK) ; Sergei Ovchinnikov (School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK; Institute of Theoretical and Mathematical Physics, Lomonosov Moscow State University, Leninskie Gory, Moscow, 119991, Russia)

We consider the classification of supersymmetric black hole solutions to five-dimensional STU gauged supergravity that admit torus symmetry. This reduces to a problem in toric Kähler geometry on the base space. We introduce the class of separable toric Kähler surfaces that unify product-toric, Calabi-toric and orthotoric Kähler surfaces, together with an associated class of separable 2-forms. We prove that any supersymmetric toric solution that is timelike, with a separable Kähler base space and Maxwell fields, outside a horizon with a compact (locally) spherical cross-section, must be locally isometric to the known black hole or its near-horizon geometry. An essential part of the proof is a near-horizon analysis which shows that the only possible separable Kähler base space is Calabi-toric. In particular, this also implies that our previous black hole uniqueness theorem for minimal gauged supergravity applies to the larger class of separable Kähler base spaces.

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      "source": "Springer", 
      "value": "We consider the classification of supersymmetric black hole solutions to five-dimensional STU gauged supergravity that admit torus symmetry. This reduces to a problem in toric K\u00e4hler geometry on the base space. We introduce the class of separable toric K\u00e4hler surfaces that unify product-toric, Calabi-toric and orthotoric K\u00e4hler surfaces, together with an associated class of separable 2-forms. We prove that any supersymmetric toric solution that is timelike, with a separable K\u00e4hler base space and Maxwell fields, outside a horizon with a compact (locally) spherical cross-section, must be locally isometric to the known black hole or its near-horizon geometry. An essential part of the proof is a near-horizon analysis which shows that the only possible separable K\u00e4hler base space is Calabi-toric. In particular, this also implies that our previous black hole uniqueness theorem for minimal gauged supergravity applies to the larger class of separable K\u00e4hler base spaces."
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Published on:
07 May 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 5
Pages 1-50
DOI:
https://doi.org/10.1007/JHEP05(2024)062
arXiv:
2311.06124
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: