2025/03/28 by Georgios Mavrogiannis, Mavrogiannis, Georgios
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2503.22077
We study the Klein--Gordon equation \Box_ga,M,lψ-μ2KGψ=0 on subextremal Kerr--de Sitter black hole backgrounds with parameters (a,M,l), where l2=\frac3Λ. We prove boundedness and Morawetz estimates assuming an appropriate mode stability statement for real frequency solutions of Carter's radial ode. Our results in particular apply in the very slowly rotating case |a|≪ M,l, and in the case where the solution~ψ is axisymmetric. This generalizes the work of Dafermos--Rodnianski \citeDR3 on Schwarzschild--de~Sitter. The boundedness and Morawetz results of the present paper will be used in our companion \citemavrogiannis2 to prove a `relatively non-degenerate integrated estimate' for subextremal Kerr--de Sitter black holes~(and as a consequence exponential decay). In a forthcoming paper \citemavrogiannis3, this will immediately yield nonlinear stability results for quasilinear wave equations on subextremal Kerr--de Sitter backgrounds.