克尔几何中的线性波：通向黑洞物理学的数学之旅
Linear Waves in the Kerr Geometry: A Mathematical Voyage to Black Hole Physics
摘要：
本文综述了Kerr时空几何中的波动动力学，Kerr时空几何是平衡旋转黑洞的数学模型。在简单介绍Kerr度规的基础上，我们回顾了一般自旋$s=0, 1/2, 1, 2$场的线性波动方程的可分性，这些场对应于标量场、Dirac场、电磁场和线性化的引力波。我们给出了狄拉克波和纯量波的长期动力学结果，包括大质量狄拉克场的衰变率。对于标量波，我们给出了超辐射的严格处理，并严格描述了从旋转黑洞中提取能量的机制。最后，我们讨论了Kerr度量的线性稳定性的公开问题，并给出了部分结果。
英文摘要：
This paper gives a survey of wave dynamics in the Kerr space-time geometry, the mathematical model of a rotating black hole in equilibrium. After a brief introduction to the Kerr metric, we review the separability properties of linear wave equations for fields of general spin $s=0, 1/2, 1, 2$, corresponding to scalar, Dirac, electromagnetic fields and linearized gravitational waves. We give results on the long-time dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields. For scalar waves, we give a rigorous treatment of superradiance and describe rigorously a mechanism of energy extraction from a rotating black hole. Finally, we discuss the open problem of linear stability of the Kerr metric and present partial results.
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