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Article Dans Une Revue J.Funct.Anal. Année : 2022

Sharp decay estimates for massless Dirac fields on a Schwarzschild background

Lin Zhang

Résumé

We consider the explicit asymptotic profile of massless Dirac fields on a Schwarzschild background. First, we prove for the spin s=±12 components of the Dirac field a uniform bound of a positive definite energy and an integrated local energy decay estimate from a symmetric hyperbolic wave system. Based on these estimates, we further show that these components have globally pointwise decay fv3/2sτ5/2+s as both an upper and a lower bound outside the black hole, with function f finite and explicitly expressed in terms of the initial data and the coordinates. This establishes the validity of the conjectured Price's law for massless Dirac fields outside a Schwarzschild black hole.

Dates et versions

hal-02940006 , version 1 (15-09-2020)

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Siyuan Ma, Lin Zhang. Sharp decay estimates for massless Dirac fields on a Schwarzschild background. J.Funct.Anal., 2022, 282, pp.109375. ⟨10.1016/j.jfa.2021.109375⟩. ⟨hal-02940006⟩
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