Late-time asymptotics conjecture for the linear charged wave equation on sub-extremal Reissner–Nordström spacetime

Let $g_{RN}$ be the sub-extremal Reissner–Nordström exterior metric with mass $M$ and charge $e$, where $0\leq |e|<M$, and let $r_+(M,e)=M+\sqrt{M^2-e^2}$. In an appropriate gauge, consider the linear charged wave equation

$$(g_{RN}^{-1})^{\mu\nu}\partial_\mu\partial_\nu\phi=\left(\frac{iqe}{r^2}-\frac{2M}{r^3}+\frac{2e^2}{r^4}\right)\phi+\frac{2iqe}{r}(\partial_t\phi+\partial_r\phi).$$

Late-time asymptotics conjecture. If $0<|qe|<\frac{1}{2}$, then a solution $\phi$ with generic, regular initial data obeys the asymptotics stated in the paper's sharp asymptotic results for the uncharged models, for every $r\geq r_+(M,e)$.

The claim proposes that the simplified linear charged wave model, the Maxwell–Klein–Gordon system, and the related charged scalar field model share the same late-time asymptotics. The supplied text does not establish this assertion or provide evidence resolving it.