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arXiv · 2102.11884

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

Yannis Angelopoulos·Stefanos Aretakis·Dejan Gajic
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Abstract

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. Our mechanism identifies and exploits the existence of conserved charges along null infinity via a time invertibility theory, which in turn relies on new elliptic estimates in the full black hole exterior. This framework is suitable for resolving the conflicting numerology in Kerr late-time asymptotics that appears in the numerics literature.

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Yannis Angelopoulos, Stefanos Aretakis, Dejan Gajic. 2021-02-23. Late-time tails and mode coupling of linear waves on Kerr spacetimes. https://arxiv.org/abs/2102.11884

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