德西特背景下任意自旋无质量微扰的Teukolsky方程解析解

Yao-Z Zhang
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引用次数: 1

摘要

我们给出了四维de Sitter背景下任意自旋无质量摄动的Teukolsky方程的解析解。方程的角部将分离常数固定为离散集,其解由超几何多项式给出。对于径向部分,我们导出了在极点处正则的解析幂级数解,并确定了一个超越函数,它的零点给出了波频的特征值。研究了径向方程的显式多项式解的存在性,得到了两类奇异闭型解,一类具有离散波频率,另一类具有连续频谱。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analytic solutions of the Teukolsky equation for massless perturbations of any spin in de Sitter background
We present analytic solutions to the Teukolsky equation for massless perturbations of any spin in the 4-dimensional de Sitter background. The angular part of the equation fixes the separation constant to a discrete set and its solution is given by hypergeometric polynomials. For the radial part, we derive analytic power series solution which is regular at the poles and determine a transcendental function whose zeros give the characteristic values of the wave frequency. We study the existence of explicit polynomial solutions to the radial equation and obtain two classes of singular closed-form solutions, one with discrete wave frequencies and the other with continuous frequency spectra.
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