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arXiv · 2008.11429

Sharp decay estimates for massless Dirac fields on a Schwarzschild background

Siyuan Ma·Lin Zhang
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Abstract

We consider the explicit asymptotic profile of massless Dirac fields on a Schwarzschild background. First, we prove for the spin $s=\pm \frac{1}{2}$ 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 $fv^{-3/2-s}\tau^{-5/2+s}$ 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.

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Siyuan Ma, Lin Zhang. 2020-08-26. Sharp decay estimates for massless Dirac fields on a Schwarzschild background. https://doi.org/10.1016/j.jfa.2021.109375

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