Price's law for spin fields on a Schwarzschild background

Siyuan Ma, Lin Zhang

Published 2021-04-28Version 1

In this work, we give a proof of the globally sharp asymptotic profiles for the spin-$\sfrak$ fields on a Schwarzschild background, including the scalar field $(\sfrak=0)$, the Maxwell field $(\sfrak=\pm 1)$ and the linearized gravity $(\sfrak=\pm 2)$. This confirms the conjectured Price's law in the physics literature which predicts the sharp estimates of the spin $s=\pm \sfrak$ components towards the future null infinity as well as in a compact region. The asymptotics are derived via a unified, detailed analysis of the Teukolsky master equation which is satisfied by all these components.