靠近黑洞场的静态引力场中自旋半粒子的束缚态
Bound states of spin-half particles in a static gravitational field close to the black hole field
摘要：
本文研究了近黑洞物体引力场中自旋为1/2的费米子的束缚态能级。在物体的度规变得奇异的极限下，所有的结合能都趋向于静止质量能量（即总能量接近于零）。我们提出了计算的基态能量为三个特定的内部度量（弗洛里德斯，Soffel和Schwarzschild）的频谱崩溃，并成为准连续的奇异度量极限。在达到这个极限之前，缺乏零或负能量状态会阻止粒子对的产生。因此，与库仑情况相反，在非奇异静态度规中不产生对。对于Florides和Soffel度规的奇异性发生在黑洞的极限，而对于史瓦西内部度规，它对应于无限的压力在中心。的能级谱的行为进行了讨论的上下文中的半经典近似和使用一般性质的度量。
英文摘要：
We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.
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