  We prove Price's law with an explicit leading order term for solutions
$\phi(t,x)$ of the scalar wave equation on a class of stationary asymptotically
flat $(3+1)$-dimensional spacetimes including subextremal Kerr black holes. Our
precise asymptotics in the full forward causal cone imply in particular that
$\phi(t,x)=c t^{-3}+\mathcal O(t^{-4+})$ for bounded $|x|$, where $c\in\mathbb
C$ is an explicit constant. This decay also holds along the event horizon on
Kerr spacetimes and thus renders a result by Luk-Sbierski on the linear scalar
instability of the Cauchy horizon unconditional. We moreover prove inverse
quadratic decay of the radiation field, with explicit leading order term. We
establish analogous results for scattering by stationary potentials with
inverse cubic spatial decay. On the Schwarzschild spacetime, we prove pointwise
$t^{-2 l-3}$ decay for waves with angular frequency at least $l$, and $t^{-2
l-4}$ decay for waves which are in addition initially static. This definitively
settles Price's law for linear scalar waves in full generality.
  The heart of the proof is the analysis of the resolvent at low energies.
Rather than constructing its Schwartz kernel explicitly, we proceed more
directly using the geometric microlocal approach to the limiting absorption
principle pioneered by Melrose and recently extended to the zero energy limit
by Vasy.
