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arXiv · 2111.04489

Sharp decay for Teukolsky equation in Kerr spacetimes

Siyuan Ma·Lin Zhang
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Abstract

In this work, we derive the global sharp decay, as both a lower and an upper bounds, for the spin $\pm \mathfrak{s}$ components, which are solutions to the Teukolsky equation, in the black hole exterior and on the event horizon of a slowly rotating Kerr spacetime. These estimates are generalized to any subextreme Kerr background under an integrated local energy decay estimate. Our results apply to the scalar field $(\mathfrak{s}=0)$, the Maxwell field $(\mathfrak{s}=1)$ and the linearized gravity $(\mathfrak{s}=2)$ and confirm the Price's law decay that is conjectured to be sharp. Our analyses rely on a novel global conservation law for the Teukolsky equation, and this new approach can be applied to derive the precise asymptotics for solutions to semilinear wave equations.

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Siyuan Ma, Lin Zhang. 2021-11-08. Sharp decay for Teukolsky equation in Kerr spacetimes. https://doi.org/10.1007/s00220-023-04640-w

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