We consider the explicit asymptotic profile of massless Dirac fields on a Schwarzschild background. First, we prove a uniform bound estimate for a positive definite energy and an integrated local energy decay estimate for the spin s = ±1/2 components of the Dirac field. Based on these estimates and depending on the asymptotics of the initial data, we further show these components have pointwise decay $c_1v^{−3/2−s}\tau^{−3/2+s}$ or $c_2v^{−3/2−s} \tau^{−5/2+s}$ as both an upper and a lower bound, with constants $c_1$ and $c_2$ explicitly expressed in terms of the initial data. This establishes the validity of the conjectured Price’s law for massless Dirac fields outside a Schwarzschild black hole. This talk is based on a joint work with Siyuan Ma.

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