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

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 $m_{\mathrm{KG}}^2\in [0,\Lambda \sqrt{2}]$ of squared scalar field masses that includes, in particular, the minimally coupled case $m_{\mathrm{KG}}=0$ and the conformally coupled case $m_{\mathrm{KG}}^2=\frac{2}{3}\Lambda$ (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 $m_{\mathrm{KG}}$.

arXiv comment25 pages, 1 figure. v2 includes the Klein-Gordon case