论文标题
在KERR公制中的费尔米金角本征函数上的特征值
On the eigenvalues of the fermionic angular eigenfunctions in the Kerr metric
论文作者
论文摘要
鉴于最近在线性哈密顿系统的变形理论的背景下发表的结果，我们重新考虑了与Kerr指标中DIRAC方程分离后产生的角度方程相关的特征值问题，并且我们显示了对Angular eigenvalue的准线性PDE的有效性PDE的有效性。我们还证明，不可能获得特征值的普通微分方程，在这种情况下，自变量的作用是由粒子能量或黑洞质量扮演的。最后，我们为Kerr案例中的特征值构建了新的扰动扩展，并在Kerr Naked Singularity的情况下为特征值获得了渐近公式。
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.
