Price’s Law for Spin Fields on a Schwarzschild Background

In this work, we derive the globally precise late-time asymptotics for the spin- 𝔰 fields on a Schwarzschild background, including the scalar field (𝔰=0) , the Maxwell field (𝔰=± 1) and the linearized gravity (𝔰=± 2) . The conjectured Price’s law in the physics literature which predicts the sharp rates of decay of the spin s=±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.