史瓦西背景下自旋场的普赖斯定律
Price's law for spin fields on a Schwarzschild background
AI总结：
本文在史瓦西背景下统一分析Teukolsky主方程，证明了自旋场（标量、麦克斯韦、线性化引力）的普赖斯定律，并证实自旋+1、+2分量在事件视界处具有额外衰减。
摘要：
在这项工作中，我们推导出史瓦西背景下自旋-$\mathfrak{s}$场的全局精确晚期渐近行为，包括标量场$(\mathfrak{s}=0)$、麦克斯韦场$(\mathfrak{s}=\pm 1)$和线性化引力$(\mathfrak{s}=\pm 2)$。物理文献中猜想的普赖斯定律预测了自旋$s=\pm \mathfrak{s}$分量朝向未来零无穷远以及在紧致区域内衰减的尖锐速率，该定律在此得到证明。此外，我们证实了Barack和Ori的启发式论断，即自旋$+1, +2$分量在事件视界处比猜想的普赖斯定律具有额外一阶衰减。这些渐近行为是通过对所有分量共同满足的Teukolsky主方程进行统一而详细的分析推导出来的。
英文摘要：
In this work, we derive the globally precise late-time asymptotics for the spin-$\mathfrak{s}$ fields on a Schwarzschild background, including the scalar field $(\mathfrak{s}=0)$, the Maxwell field $(\mathfrak{s}=\pm 1)$ and the linearized gravity $(\mathfrak{s}=\pm 2)$. The conjectured Price's law in the physics literature which predicts the sharp rates of decay of the spin $s=\pm \mathfrak{s}$ components towards the future null infinity as well as in a compact region is shown. Further, we confirm the heuristic claim by Barack and Ori that the spin $+1, +2$ components have an extra power of decay at the event horizon than the conjectured Price's law. The asymptotics are derived via a unified, detailed analysis of the Teukolsky master equation that is satisfied by all these components.
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