Late-time tails and mode coupling of linear waves on Kerr spacetimes

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We provide a rigorous derivation of the precise late-time asymptotics for solutions to the scalar wave equation on subextremal Kerr backgrounds, including the asymptotics for projections to angular frequencies $\ell\geq 1$ and $\ell\geq 2$.

• The $\ell$-dependent asymptotics on Kerr spacetimes differ significantly from the non-rotating Schwarzschild setting ("Price's law").
• The main differences with Schwarzschild are slower decay rates for higher angular frequencies and oscillations along the null generators of the event horizon.
• We introduce a physical space-based method that resolves the following two main difficulties for establishing $\ell$-dependent asymptotics in the Kerr setting: 1) the coupling of angular modes and 2) a loss of ellipticity in the ergoregion.