Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry
Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry
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克尔-纽曼黑洞几何中大质量狄拉克粒子的衰变率和概率估计¶
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
S. Yau
中科院分区：
文献类型：
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作者：
F. Finster;N. Kamran;J. Smoller;S. Yau
摘要考虑了非极值Kerr-Newman几何中的大质量Dirac方程，在视界外具有紧致支持和有界角动量的光滑初始数据的Cauchy问题。我们证明了狄拉克波函数在$L^\infty_{\mbox{\scriptsize{loc}}}$中至少以t - 5/6的速率衰减。对于一般的初始数据，这种衰减速度非常快。我们推导出狄拉克粒子逃逸到无穷远的概率p的公式。对于初始数据的各种条件，我们证明了p = 0,1或0 < p < 1。这些证明是基于对在[4]中构造的狄拉克传播子的精细分析。
Abstract: The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in $L^\infty_{\mbox{\scriptsize{loc}}}$ at least at the rate t−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4].