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arXiv · 2608.25868

Mode stability for the Klein-Gordon equation on subextremal Kerr-de Sitter spacetimes

Peter Hintz
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Abstract

We prove mode stability for the Klein-Gordon equation on Kerr-de Sitter black hole spacetimes in the full subextremal range and for the range $m_{\rm KG}^2\in[0,\Lambda\sqrt{2}]$ of squared scalar field masses that includes, in particular, the minimally coupled case $m_{\rm KG}=0$ and the conformally coupled case $m_{\rm KG}^2=\frac{2}{3}\Lambda$ (i.e., the Teukolsky equation for spin $0$). In combination with recent work by Petersen-Vasy, this proves, unconditionally, that sufficiently regular solutions of the scalar wave equation decay exponentially fast to constants, and in fact to zero for nonzero $m_{\rm KG}$.

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Peter Hintz. 2026-08-26. Mode stability for the Klein-Gordon equation on subextremal Kerr-de Sitter spacetimes. https://arxiv.org/abs/2608.25868

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