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arXiv · 2104.13809

Price's law for spin fields on a Schwarzschild background

Siyuan Ma·Lin Zhang
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Abstract

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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Siyuan Ma, Lin Zhang. 2021-04-28. Price's law for spin fields on a Schwarzschild background. https://doi.org/10.1007/s40818-022-00139-0

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