论文标题
Schwarzschild背景上无质量狄拉克场的急剧衰减估计值
Sharp decay estimates for massless Dirac fields on a Schwarzschild background
论文作者
论文摘要
我们考虑在施瓦茨柴尔德背景下无质量迪拉克场的显式渐近概况。首先，我们证明了旋转$ s = \ pm \ frac {1} {2} $组分的dirac场的成分是一个正确定能量的均匀绑定，并且是从对称性高压波系统中进行的局部能量衰减估计值。根据这些估计，我们进一步表明，这些组件在全球呈衰减$ fv^{ - 3/2-s}τ^{ - 5/2+s} $中，作为黑洞外部和下限，具有$ f $有限的函数$ f $有限且以初始数据和坐标为单位。这确立了猜想的价格定律在施瓦茨柴尔德黑洞外的无质迪拉克田地的有效性。
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 $fv^{-3/2-s}τ^{-5/2+s}$ 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.
