在壳振幅与黑洞微扰：精确的雷斯纳-诺德斯特龙（Reissner-Nordström, RN）混合
On-Shell Amplitudes and Black-Hole Perturbations: Exact Reissner-Nordström Mixing
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中文总结 AI 辅助
该研究探讨平直空间在壳振幅能否确定耦合黑洞微扰的通道基，以RN黑洞的电磁与引力微扰为对象，通过分波投影等方法揭示相关投影算子的性质，为旋转黑洞的推广提供了基础。
中文摘要 AI 辅助
平直空间的在壳振幅能否确定耦合黑洞微扰问题的通道基？我们针对雷斯纳-诺德斯特龙（Reissner-Nordström, RN）黑洞的电磁与引力微扰这一问题展开研究。我们将重带电源的最小耦合光子-引力子树图振幅整理为一个2×2的通道空间矩阵，并进行宇称分解的Jacob-Wick分波投影。对于所有辐射多极ℓ≥2以及两个宇称扇区，我们证明无迹的固定源分波矩阵与无迹的Moncrief耦合矩阵精确成正比，因此会选择相同的常数谱投影算子。通过一阶玻恩匹配，这些振幅在主导阶r⁻³弱场势中确定了相同的本征空间，但无法确定完整的径向势。以精确的经典RN势作为独立的弯曲背景输入，我们证明这些投影算子在整个径向域内持续存在。我们还显式保留了有限质量效应至𝒪(ω/m)阶，发现其与Moncrief耦合矩阵存在非零对易子，这表明RN投影算子的对齐会被真实的两体反冲效应破坏。作为向旋转情况推广的第一步，我们进一步从最小耦合狄拉克振幅中提取出与表示无关的线性自旋项。我们发现完整的树图通道矩阵可通过单一线性自旋修饰因子分解，而形式上的J=2块无法保持不变的RN投影算子。这一受限结果不构成对克尔-纽曼（Kerr-Newman）可分离性的检验，但它表明旋转推广必须考虑自旋诱导的角模式混合。我们期望该在壳方法可扩展至具有两个渐近通道的更一般长程散射系统。
英文摘要
Can flat-space on-shell amplitudes determine the channel basis of a coupled black-hole perturbation problem? We address this question for electromagnetic and gravitational perturbations of a Reissner-Nordström (RN) black-hole. We organize the minimally coupled photon-graviton tree amplitudes off a heavy charged source into a $2\times 2$ channel-space matrix and perform a parity-resolved Jacob-Wick partial-wave projection. For every radiative multipole $\ell \geq 2$ and in both parity sectors, we show that the trace-free fixed-source partial-wave matrix is exactly proportional to the trace-free Moncrief coupling matrix, and therefore selects the same constant spectral projectors. Through a first-Born matching, the amplitudes determine the same eigenspaces in the leading $r^{-3}$ weak-field potential, but not the complete radial potentials. Using the exact classical RN potentials as independent curved-background input, we show that these projectors persist throughout the full radial domain. We also explicitly retain finite-mass effects through $\mathcal{O}(ω/m)$, finding a nonvanishing commutator with the Moncrief coupling matrix, which shows that the RN-projector alignment is spoiled by genuine two-body recoil effects. As a first step toward rotation, we further extract the representation-independent linear-spin term from a minimally coupled Dirac amplitude. We find that the complete tree-level channel matrix factorizes with a single linear-spin dressing, while the formal $J=2$ block fails to preserve the unchanged RN projectors. This restricted result does not constitute a test of Kerr-Newman separability, but it indicates that a rotating generalization must account for spin-induced angular-mode mixing. We expect that this on-shell method can be extended to more general long-range scattering systems with two asymptotic channels.
