AI 中文总结
本文在洛伦兹破缺KR引力的旋转带电黑洞几何中，研究大质量中性狄拉克场准束缚态，推导边界条件与复谱，发现KR参数对实频率和衰变率的影响存在鲁棒的能级重排现象。
AI 中文摘要
我们研究洛伦兹破缺Kalb-Ramond（KR）引力中，纽曼-贾尼斯生成的旋转带电几何里的大质量中性狄拉克场的准束缚态。我们未假设克尔分离在形变中保留，而是先将度规重写为四维离壳卡特形式，对应的主闭合共形基林-亚诺张量提供了分离无挠、最小耦合狄拉克方程所需的隐藏对称性。我们推导了视界和大半径边界条件，包括非闵氏渐近归一化，并通过耦合角向和矩阵径向连分数确定复谱。该代码可复现克尔谱，并通过截断研究和独立双侧径向积分验证。在固定度规参数的扫描中，增大KR参数会使多数实频率向质量阈值移动，并降低多数衰变率；然而这些趋势并非不变，因为同一变化会同时改变渐近势尺度和极端性距离。在固定这两个量的扫描中，绝对基态趋势改变，但保留了最大m、j=3/2、ℓ=1对的实频率排序反转，交叉位置随归一化惯例变化。因此，在该背景族中，能级重排比结合能或寿命的单独单调趋势更具鲁棒性。
英文摘要
We study quasibound states of a massive neutral Dirac field in the Newman-Janis-generated rotating charged geometry used in Lorentz-violating Kalb-Ramond (KR) gravity. Rather than assuming that the Kerr separation survives the deformation, we first recast the metric in four-dimensional off-shell Carter form. The corresponding principal closed conformal Killing-Yano tensor then provides the hidden symmetry needed to separate the torsion-free, minimally coupled Dirac equation. We derive the horizon and large-radius boundary conditions, including the non-Minkowskian asymptotic normalization, and determine the complex spectrum from coupled angular and matrix radial continued fractions. The code reproduces the Kerr spectrum and is checked by truncation studies and independent two-sided radial integrations. In scans at fixed metric parameters, increasing the KR parameter moves most real frequencies toward the mass threshold and reduces most decay rates. These trends are not invariant, however, because the same variation changes both the asymptotic potential scale and the distance from extremality. A scan in which these two quantities are held fixed changes the absolute ground-state trend but preserves a reversal in the real-frequency ordering of the maximal-$m$, $j=3/2$, $\ell=1$ pair. The location of the crossing shifts with the normalization convention. Thus the level reordering is more robust than the individual monotonic trends in binding energy or lifetime within this background family.
