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arXiv · 2608.02259

Hidden Symmetry of Kerr-deSitter from Manifest Symmetry of Painlev\'e VI

Stefan Hollands·Akihiro Ishibashi·Jochen Zahn
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Abstract

We show that the recently discovered ``mass symmetries" of the radial Teukolsky equation for Kerr-deSitter black holes can be understood from a corresponding symmetry of the Painlev\'e VI equation via the classical theory of ``isomonodromic deformations". It is known that a subset of the mass symmetries transforms the Teukolsky equation to a wave equation on a ``dual" Lorentzian spacetime. We find that this dual spacetime again represents a black hole, and use this insight to re-obtain a previously known partial mode stability result in a geometric manner. Further special geometric features of the dual spacetime are pointed out.

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Stefan Hollands, Akihiro Ishibashi, Jochen Zahn. 2026-08-03. Hidden Symmetry of Kerr-deSitter from Manifest Symmetry of Painlev\'e VI. https://arxiv.org/abs/2608.02259

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