Price’s Law for Spin Fields on a Schwarzschild Background
Tóm tắt
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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