Mode analysis for the linearized Einstein equations on the Kerr metric : the large $\mathfrak{a}$ case

Understand

We give a complete analysis of mode solutions for the linearized Einstein equations and the $1-$form wave operator on the Kerr metric in the large $\mathfrak{a}$ case.

• By mode solutions we mean solutions of the form $e^{-it_*\sigma}\tilde{h}(r,\theta,\varphi)$ where $t_*$ is a suitable time variable.
• The corresponding Fourier transformed $1-$form wave operator and linearized Einstein operator are shown to be Fredholm between suitable function spaces and $\tilde{h}$ has to lie in the domain of these operators.
• These spaces are constructed following the general framework of Vasy.