标题： 关于克尔度规中费米子角本征函数的本征值 显示英文标题

标题： On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric

摘要： 鉴于最近在线性哈密顿系统变形理论背景下发表的一个结果，我们重新考虑了在克尔度规中分离狄拉克方程后出现的角方程相关的特征值问题，并展示了如何有效地推导出角特征值的准线性一阶偏微分方程。 我们还证明了无法得到一个常微分方程来描述特征值，其中粒子能量或黑洞质量作为自变量。 最后，我们为克尔情况下的特征值构造了新的摄动展开式，并得到了克尔裸奇点情况下特征值的渐近公式。 显示英文摘要

摘要： In view of a result recently published in the context of deformation theory of linear Hamiltonian systems, we reconsider the eigenvalue problem associated to the angular equation arising after the separation of the Dirac equation in the Kerr metric and we show how efficiently a quasi-linear first order PDE for the angular eigenvalues can be derived. We also prove that it is not possible to obtain an ordinary differential equation for the eigenvalues where the role of the independent variable is played by the particle energy or the black hole mass. Finally, we construct new perturbative expansions for the eigenvalues in the Kerr case and obtain an asymptotic formula for the eigenvalues in the case of a Kerr naked singularity.