Price’s Law and Precise Late-Time Asymptotics for Subextremal Reissner–Nordström Black Holes

In this paper, we prove precise late-time asymptotics for solutions to the wave equation supported on angular frequencies greater or equal to \(\ell \) on the domain of outer communications of subextremal Reissner–Nordstr?m spacetimes up to and including the event horizon. Our asymptotics yield, in particular, sharp upper and lower decay rates which are consistent with Price’s law on such backgrounds. We present a theory for inverting the time operator and derive an explicit representation of the leading-order asymptotic coefficient in terms of the Newman–Penrose charges at null infinity associated with the time integrals. Our method is based on purely physical space techniques. For each angular frequency \(\ell \), we establish a sharp hierarchy of r-weighted radially commuted estimates with length \(2\ell +5\). We complement this hierarchy with a novel hierarchy of weighted elliptic estimates of length \(\ell +1\).