Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions
Analytic Solutions of the Teukolsky Equation and Their Low Frequency Expansions
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Teukolsky方程的解析解及其低频展开式
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
E. Takasugi
中科院分区：
文献类型：
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作者：
S. Mano;Hisao Suzuki;E. Takasugi
克尔几何中 Teukolsky 方程的解析解以一系列超几何函数和库仑波函数的形式呈现。这些解决方案之间的关系已建立。这些解提供了一种非常强大的方法，不仅可以用于检查解和物理量应用时的一般属性，而且还可以用于数值计算。解在小参数 $epsilon 相当于 2Momega$ 的展开中给出，$M$ 是黑洞的质量，对应于 $G$ 的后明可夫斯基展开和后牛顿展开，当它们应用于围绕黑洞的圆形轨道上的粒子的引力辐射时。预计这些解决方案将成为构建LIGO和VIRGO项目理论模板的有力武器。
Analytic solutions of the Teukolsky equation in Kerr geometries are presented in the form of series of hypergeometric functions and Coulomb wave functions. Relations between these solutions are established. The solutions provide a very powerful method not only for examining the general properties of solutions and physical quantities when they are applied to, but also for numerical computations. The solutions are given in the expansion of a small parameter $epsilon equiv 2Momega$, $M$ being the mass of black hole, which corresponds to Post-Minkowski expansion by $G$ and to post-Newtonian expansion when they are applied to the gravitational radiation from a particle in circular orbit around a black hole. It is expected that these solutions will become a powerful weapon to construct the theoretical template towards LIGO and VIRGO projects.