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Article Dans Une Revue Commun.Math.Phys. Année : 2023

Sharp decay for Teukolsky equation in Kerr spacetimes

Lin Zhang

Résumé

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.

Dates et versions

hal-03441115 , version 1 (22-11-2021)

Identifiants

Citer

Siyuan Ma, Lin Zhang. Sharp decay for Teukolsky equation in Kerr spacetimes. Commun.Math.Phys., 2023, 401 (1), pp.333-434. ⟨10.1007/s00220-023-04640-w⟩. ⟨hal-03441115⟩
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