The massive Dirac equation in Kerr geometry: separability in Eddington–Finkelstein-type coordinates and asymptotics
The massive Dirac equation in Kerr geometry: separability in Eddington–Finkelstein-type coordinates and asymptotics
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DOI：
10.1007/s10714-017-2194-y
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发表时间：
2015-06
影响因子：
2.8
通讯作者：
C. Röken
中科院分区：
文献类型：
--
作者：
C. Röken
本文证明了在视界穿透的高阶Eddington-Finkelstein型坐标系下非极端Kerr几何中的有质量Dirac方程的可分性。为此，克尔几何描述的卡特四分体和狄拉克旋量和矩阵给出了手征纽曼-彭罗斯二分体表示。应用钱德拉塞卡模式假设，狄拉克方程被分成径向和角度常微分方程组。渐近径向解在无穷远，事件视界，柯西视界明确推导。通过误差估计分析了它们的衰变。此外，还讨论了角系统的本征函数和本征值。最后，作为应用，研究了Dirac波被Kerr黑洞引力场的散射。这项工作提供了一个哈密顿制定的大规模狄拉克方程在克尔几何中的视界穿透坐标和建设的功能解析积分表示的狄拉克传播。
The separability of the massive Dirac equation in the non-extreme Kerr geometry in horizon-penetrating advanced Eddington–Finkelstein-type coordinates is shown. To this end, Kerr geometry is described by a Carter tetrad and the Dirac spinors and matrices are given in a chiral Newman–Penrose dyad representation. Applying Chandrasekhar’s mode ansatz, the Dirac equation is separated into systems of radial and angular ordinary differential equations. Asymptotic radial solutions at infinity, the event horizon, and the Cauchy horizon are explicitly derived. Their decay is analyzed by means of error estimates. Moreover, the eigenfunctions and eigenvalues of the angular system are discussed. Finally, as an application, the scattering of Dirac waves by the gravitational field of a Kerr black hole is studied. This work provides the basis for a Hamiltonian formulation of the massive Dirac equation in Kerr geometry in horizon-penetrating coordinates and for the construction of a functional analytic integral representation of the Dirac propagator.