Nonexistence of time‐periodic solutions of the Dirac equation in an axisymmetric black hole geometry
Nonexistence of time‐periodic solutions of the Dirac equation in an axisymmetric black hole geometry
复制标题
轴对称黑洞几何中狄拉克方程的时间周期解不存在
DOI：
10.1002/(sici)1097-0312(200007)53:7
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发表时间：
1999
影响因子：
3
通讯作者：
S. Yau
中科院分区：
文献类型：
--
作者：
F. Finster;N. Kamran;J. Smoller;S. Yau
我们证明了在非极端Kerr - Newman黑洞几何中狄拉克方程没有可归一化的时间周期解。一个关键的工具是钱德拉塞卡对该几何中狄拉克方程的分离。在一类更一般的稳态轴对称度量中，我们建立了类似的不存在定理，其中狄拉克方程已知是可分离的。这些结果表明，与大质量粒子轨道的经典情况相反，量子力学的狄拉克粒子要么消失在黑洞中，要么逃逸到宇宙中
We prove that in the non extreme Kerr Newman black hole geometry the Dirac equation has no normalizable time periodic solutions A key tool is Chandrasekhar s separation of the Dirac equation in this geometry A similar non existence theorem is established in a more general class of stationary axisymmetric metrics in which the Dirac equation is known to be separable These results indicate that in contrast with the classical situation of massive particle orbits a quantum mechanical Dirac particle must either disappear into the black hole or escape to in nity