2025/03/28 by Mavrogiannis, Georgios
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2503.22090
We study the Klein--Gordon equation \Boxψ-μ2KGψ=0 on subextremal Kerr de Sitter black hole backgrounds with parameters (a,M,l), where l2=\frac3Λ. We prove a "relatively non degenerate integrated" decay estimate assuming an appropriate mode stability statement for real frequency solutions of Carter's radial ode. Our results, in particular, apply unconditionally in the very slowly rotating case |a|≪ M,l, and in the case where ψ is axisymmetric. Exponential decay for ψ to a constant is a consequence of this estimate. To prove our result, we introduce a novel pseudodifferential commutation operator G that generalizes our previous purely physical space commutation \citemavrogiannis and we use it in conjunction with the Morawetz estimate of our companion \citemavrogiannis4. This pseudodifferential operator is defined using Fourier decomposition with respect to time frequencies ω and azimuthal frequencies m, but does not require Carter's full separation.