Ma, Siyuan; Zhang, Lin Sharp decay estimates for massless Dirac fields on a Schwarzschild background. (English) Zbl 1503.83009 J. Funct. Anal. 282, No. 6, Article ID 109375, 112 p. (2022). Summary: 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 \(f v^{- 3 / 2 - s} \tau^{- 5 / 2 + s}\) 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. Cited in 9 Documents MSC: 83C57 Black holes 81R25 Spinor and twistor methods applied to problems in quantum theory 81U90 Particle decays 47A10 Spectrum, resolvent 35L05 Wave equation 58J47 Propagation of singularities; initial value problems on manifolds Keywords:massless Dirac; Price’s law; sharp decay; Schwarzschild background PDFBibTeX XMLCite \textit{S. Ma} and \textit{L. Zhang}, J. Funct. Anal. 282, No. 6, Article ID 109375, 112 p. (2022; Zbl 1503.83009) Full Text: DOI arXiv References: [1] Andersson, Lars; Bäckdahl, Thomas; Blue, Pieter, Decay of solutions to the Maxwell equation on the Schwarzschild background, Class. Quantum Gravity, 33, 8, Article 085010 pp. (2016) · Zbl 1338.83093 [2] Andersson, Lars; Bäckdahl, Thomas; Blue, Pieter; Ma, Siyuan, Stability for linearized gravity on the Kerr spacetime (2019), arXiv preprint [3] Andersson, Lars; Blue, Pieter, Hidden symmetries and decay for the wave equation on the Kerr spacetime, Ann. 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