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Free keywords:
Mathematics, Analysis of PDEs, math.AP,General Relativity and Quantum Cosmology, gr-qc,
Abstract:
In this work, we give a proof of the globally sharp asymptotic profiles 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 estimates 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.
