论文标题
Korteweg-de Vries积分的黑洞灰体因素：理论
Black Hole Greybody Factors from Korteweg-de Vries Integrals: Theory
论文作者
论文摘要
可以用具有潜力的波动类型的主方程来描述扰动的非旋转黑洞（BHS）的动力学。在频域中，主方程成为时间独立的schrödinger方程，没有离散频谱。最近已经表明，这些波动方程具有无限数量的对称性，与Korteweg-de Vries（KDV）方程无限层次结构相对应。因此，对于所有可以考虑的所有不同主方程，无限的相关保守量（KDV积分）都是相同的。在本文中，我们表明，表征连续光谱的BH散射反射和传输系数可以通过矩问题充分确定，以使KDV积分仅根据反射系数提供分布函数的力量。我们还讨论了解决方案问题的存在和独特性，解决时刻问题的策略，最后显示了Pöschl-Teller潜力的情况，可以通过分析进行所有步骤。
The dynamics of perturbed non-rotating black holes (BHs) can be described in terms of master equations of the wave type with a potential. In the frequency domain, the master equations become time-independent Schrödinger equations with no discrete spectrum. It has been recently shown that these wave equations possess an infinite number of symmetries that correspond to the flow of the infinite hierarchy of Korteweg-de Vries (KdV) equations. As a consequence, the infinite set of associated conserved quantities, the KdV integrals, are the same for all the different master equations that we can consider. In this paper we show that the BH scattering reflection and transmission coefficients characterizing the continuous spectrum can be fully determined via a moment problem, in such a way that the KdV integrals provide the momenta of a distribution function depending only on the reflection coefficient. We also discuss the existence and uniqueness of solutions, strategies to solve the moment problem, and finally show the case of the Pöschl-Teller potential where all the steps can be carried out analytically.
