Price's law and precise late-time asymptotics for subextremal Reissner-Nordstr\"om black holes

TL;DR

This paper establishes precise late-time decay rates for wave solutions on subextremal Reissner-Nordström black holes, confirming Price's law and providing explicit asymptotic coefficients via physical space methods.

Contribution

It introduces a new hierarchy of $r$-weighted estimates and an explicit representation of asymptotic coefficients based on Newman-Penrose charges.

Findings

Confirmed sharp decay rates consistent with Price's law.

Derived explicit asymptotic coefficients in terms of Newman-Penrose charges.

Established a hierarchy of weighted estimates for each angular frequency.

Abstract

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\"om 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 $\ell+1$.