Conditional charged-scalar flux amplification

Given: The adopted fixed-background scalar model, the exact subextremal electric RN scattering conventions, and an admitted mode with the stated coefficients and frequency conditions.

Fixed-background charged scalar regime: the scalar is a classical massless minimally coupled field on prescribed RN-form background data, with its stress omitted from the background equations; its adopted energy tensor is the symmetric tensor of the local mathematical definition.

Massless charged-scalar radial scattering data: $A_t=-Q\mathrm{/}r$, ${\mathrm{\Phi }}_H={\lim }_{r\to \mathrm{\infty }}{A}_t(r)-{\lim }_{r\downarrow r_{+}}{A}_t(r)=Q\mathrm{/}{r}_{+}$, ${\omega }_H=\omega -e{\mathrm{\Phi }}_H$, and the normalized scattering mode has unit incoming radial amplitude with only the ingoing branch at the future horizon. The definition asserts no scattering-solution existence.

Exact charged scattering Wronskian flux identity: for each admitted mode, $\mathrm{\mid }R{\mathrm{\mid }}^2=1-\frac{\omega -eQ\mathrm{/}{r}_{+}}{\omega }\mathrm{\mid }T{\mathrm{\mid }}^2$.

Asymptotic time-translation flux of a charged scalar mode: for these asymptotics, ${\mathcal{P}}_{\mathrm{r}\mathrm{e}\mathrm{f}}\mathrm{/}{\mathcal{P}}_{\mathrm{i}\mathrm{n}}=\mathrm{\mid }R{\mathrm{\mid }}^2$ and ${\mathcal{P}}_{\mathrm{i}\mathrm{n}}=2{\omega }^2\mathrm{\mid }{A}_{\mathrm{i}\mathrm{n}}{\mathrm{\mid }}^2>0$.

The mode is admitted, $\omega >0$, $0<\omega <e{\mathrm{\Phi }}_H$, and $T\mathrm{\ne }0$. These are conditional inputs, not an existence or empirical claim.