Bound state solutions of the Dirac equation in the extreme Kerr geometry
Bound state solutions of the Dirac equation in the extreme Kerr geometry
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DOI：
10.1002/mana.200410205
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发表时间：
2004-01-01
影响因子：
1
通讯作者：
Schmid, H
中科院分区：
文献类型：
--
作者：
Schmid, H
本文考虑质量为M、角动量为J的极端Kerr黑洞背景中Dirac方程的束缚态解，即可归一化的时间周期解。证明了对于每个方位向量子数k和J值，Dirac方程都有一个束缚态解，并且这种Dirac粒子的能量由omega=-Km/2j唯一地决定。此外，我们还证明了极限Kerr-Newman几何中束束态存在的充要条件，并给出了径向本征函数的拉盖尔多项式的显式表示。(C)2004年威利-VCH威拉格有限公司，温海姆KGaA公司。
In this paper we consider bound state solutions, i.e., normalizable time-periodic solutions of the Dirac equation in an extreme Kerr black hole background with mass M and angular momentum J. It is shown that for each azimuthal quantum number k and for particular values of J the Dirac equation has a bound state solution, and that the energy of this Dirac particle is uniquely determined by omega = -kM/2J. Moreover, we prove a necessary and sufficient condition for the existence of bound states in the extreme Kerr-Newman geometry, and we give an explicit expression for the radial eigenfunctions in terms of Laguerre polynomials. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.