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arXiv 0810.1642gr-qc
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荷电de-Sitter黑洞流形背景下的大质量Dirac粒子

Massive Dirac particles on the background of charged de-Sitter black hole manifolds

F. Belgiorno, S. L. Cacciatori

摘要:

研究了带电de-Sitter黑洞背景下大质量Dirac场的行为。所有的黑洞的几何形状,包括Reissner-Nordström-de-Sitter的情况下,Nariai的情况下,和超冷的情况下考虑。我们首先讨论了在给定的背景下Dirac哈密顿量的量子力学束缚态的存在性。在这方面,我们表明,在所有情况下,没有束缚态是允许的,这也相当于狄拉克方程的规范化的时间周期解的不存在。这个量子结果与经典物理相反,即使在极端情况下也是成立的。此外,我们将注意力转移到黑洞的量子放电这个非常有趣的问题上。根据Damour-Deruelle-Ruffini方法,我们证明了正负连续能态之间的能级交叉是导致黑洞放电的量子不稳定性的信号,并在Nariai几何和超冷几何的情况下,在WKB近似下计算了与放电过程有关的透射系数.

英文摘要:

We consider the behavior of massive Dirac fields on the background of a charged de-Sitter black hole. All black hole geometries are taken into account, including the Reissner-Nordström-de-Sitter one, the Nariai case and the ultracold case. Our focus is at first on the existence of bound quantum mechanical states for the Dirac Hamiltonian on the given backgrounds. In this respect, we show that in all cases no bound state is allowed, which amounts also to the non-existence of normalizable time-periodic solutions of the Dirac equation. This quantum result is in contrast to classical physics, and it is shown to hold true even for extremal cases. Furthermore, we shift our attention on the very interesting problem of the quantum discharge of the black holes. Following Damour-Deruelle-Ruffini approach, we show that the existence of level-crossing between positive and negative continuous energy states is a signal of the quantum instability leading to the discharge of the black hole, and in the cases of the Nariai geometry and of the ultracold geometries we also calculate in WKB approximation the transmission coefficient related to the discharge process.

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