阈值渐进行为与巨质量Maxwell场在亚极端Reissner--Nordström外部的衰减
Threshold asymptotics and decay for massive Maxwell on subextremal Reissner--Nordström
AI总结：
研究亚极端Reissner--Nordström外部中性巨质量Maxwell（Proca）方程的阈值渐进行为与衰减，通过球面谐波分解，偶极子部分形成2×2系统，证明其在空间无穷远处的精确渐近极化分裂，并获得晚期时间阈值。
摘要：
我们研究亚极端Reissner--Nordström外部中性巨质量Maxwell（Proca）方程的阈值渐进行为与衰减。通过球面谐波分解，奇极子部分为标量，偶极子部分仍为真正的耦合2×2系统。我们的起点是该偶极子系统在空间无穷远处具有精确的渐近极化分裂。三个由此产生的通道携带有效的角动量ℓ-1、ℓ和ℓ+1，这些正是支配晚期时间阈值的指数。对于每个固定的角动量，我们为截断余子空间发展了阈值谱理论。我们证明了在质量分支割线上的解析延拓，排除了上半平面模式和阈值共振，获得了分支割线跃迁的显式小和大库仑展开式。反转此跃迁得到极化解析的中间尾部以及普遍的非常晚期t^{-5/6}分支割线定律。在全场水平上，高阶角正则性允许我们在紧致径向集上求和模态的主导项，获得Proca场辐射分支割线成分的双区域渐近展开式，具有显式系数场和定量余项。我们还分析了由稳定时间样 trapping 产生的准束缚共振分支，证明残差和重建界，推导出完全自洽的双极包估计。结果，未分裂的Proca场服从对数紧致区域衰减，而辐射分支割线成分保留显式多项式渐近性和显式主导系数。
英文摘要：
We study the neutral massive Maxwell (Proca) equation on subextremal Reissner--Nordström exteriors. After spherical-harmonic decomposition, the odd sector is scalar, while the even sector remains a genuinely coupled $2\times2$ system. Our starting point is that this even system admits an exact asymptotic polarization splitting at spatial infinity. The three resulting channels carry effective angular momenta $\ell-1$, $\ell$, and $\ell+1$, and these are precisely the indices that govern the late-time thresholds. % For each fixed angular momentum we develop a threshold spectral theory for the cut-off resolvent. We prove meromorphic continuation across the massive branch cut, rule out upper-half-plane modes and threshold resonances, and obtain explicit small- and large-Coulomb expansions for the branch-cut jump. Inverting this jump yields polarization-resolved intermediate tails together with the universal very-late $t^{-5/6}$ branch-cut law. % At the full-field level, high-order angular regularity allows us to sum the modewise leading terms on compact radial sets and obtain a two-regime asymptotic expansion for the radiative branch-cut component of the Proca field, with explicit coefficient fields and quantitative remainders. We also analyze the quasibound resonance branches created by stable timelike trapping, prove residue and reconstruction bounds, and derive a fully self-contained dyadic packet estimate. As a result, the unsplit full Proca field obeys logarithmic compact-region decay, while the radiative branch-cut contribution retains explicit polynomial asymptotics and explicit leading coefficients.
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