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arXiv 2307.14616gr-qc
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D型黑洞中引力、电磁和标量微扰的辐射通量:一种精确方法

Radiation fluxes of gravitational, electromagnetic, and scalar perturbations in type-D black holes: an exact approach

Changkai Chen, Jiliang Jing

AI总结:

本研究提出一种求解带源Teukolsky方程的新方法,利用合流Heun函数首次得到D型黑洞微扰方程的无约束精确波解,经Schwarzschild黑洞辐射计算验证,该解相比现有方法显著提升了计算精度与效率。

摘要:

我们提出了一种新方法,通过求解带源的Teukolsky(特科尔斯基)方程,来计算D型黑洞任意微扰场在无穷远和事件视界处的辐射通量。我们首次利用合流Heun(休恩)函数,得到了Teukolsky方程的入射波和出射波精确解,这得益于我们推导了合流Heun函数在无穷远处的渐近解析表达式。值得注意的是,这些精确解不受低频、弱场等任何条件约束。为验证正确性,我们将这些精确解应用于计算Schwarzschild(史瓦西)黑洞的引力、电磁和标量辐射。数值结果表明,与23阶后牛顿展开及Mano-Suzuki-Takasugi(真野-铃木-高杉)方法相比,所提出的精确解显著提升了计算精度和效率。

英文摘要:

We present a novel method that solves Teukolsky equations with the source to calculate radiation fluxes at infinity and event horizon for any perturbation fields of type-D black holes. For the first time, we use the confluent Heun function to obtain the exact solutions of ingoing and outgoing waves for the Teukolsky equation. This benefits from our derivation of the asymptotic analytic expression of the confluent Heun function at infinity. It is interesting to note that these exact solutions are not subject to any constraints, such as low-frequency and weak-field. To illustrate the correctness, we apply these exact solutions to calculate the gravitational, electromagnetic, and scalar radiations of the Schwarzschild black hole. Numerical results show that the proposed exact solution appreciably improves the computational accuracy and efficiency compared with the 23rd post-Newtonian order expansion and the Mano-Suzuki-Takasugi method.

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