AI 中文总结
研究将谱PINN求解器扩展用于计算克尔 - 纽曼准正则模，通过求解耦合主偏微分方程组实现。对比公开数据集得出误差，计算出相关数据集，首次表征矢量主导光子球分支，应用其观察特征值排斥现象并预测黑洞荷质比约束。
AI 中文摘要
我们将谱PINN求解器扩展到克尔 - 纽曼准正则模的计算，通过应用它来求解两个耦合主偏微分方程组，从不带电克尔极限的单个可分离方程推进到真正的双场耦合问题。引力场和电磁场之间的耦合产生了两类解：与克尔相关的光子球解和与克尔极限无关的近视界解，每类解根据主导场有两个分支。与公开数据集对比显示，最坏情况下相对频率误差约为\(10^{-4}\)，多数情况约为\(10^{-7}\)。计算的公开数据集涵盖了五个光子球模、两个基本的引力主导的近视界模，首次计算并系统表征了矢量主导的光子球分支。我们应用该数据集观察到迪亚斯等人报道的特征值排斥现象，排除了解析域内的极化间排斥，并预测了爱因斯坦望远镜对黑洞荷质比的约束。
英文摘要
We extend our \texttt{SpectralPINN} solver to the computation of Kerr-Newman quasinormal modes by applying it to solve the system of two coupled master PDEs -- advancing from the single, separable equation of the uncharged Kerr limit to a genuinely coupled two-field problem. The coupling between the gravitational and electromagnetic fields gives rise to two families of solutions: the photon-sphere, connecting with Kerr; and near-horizon, disconnected from the Kerr limit, each with two branches of solutions depending on the leading field: the gravitational- and vector-led. Benchmarking against publicly available datasets shows relative frequency errors of $\sim 10^{-4}$ worst case and $\sim10^{-7}$ for most cases. The computed public dataset spans five photon-sphere modes, both gravitational- and vector-led, up to $\ell=4$, as well as two fundamental gravitational-led near-horizon modes. The vector-led photon-sphere branch is computed and systematically characterized for the first time. We apply the dataset and observe the onset of the eigenvalue repulsion reported by Dias \textit{et al.}, to exclude an inter-polarization repulsion within the resolved domain, and to forecast Einstein Telescope constraints on the black-hole charge-to-mass ratio.
Comments24 pages, 11 figures, public dataset of 12 Kerr-Newman QNM mode branches at Zenodo: 10.5281/zenodo.21359120
