Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics
Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics
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DOI：
10.1103/physrevd.2.2141
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发表时间：
1969
影响因子：
5
通讯作者：
F. Zerilli
中科院分区：
文献类型：
--
作者：
F. Zerilli
我们关心的是当一颗星星福尔斯落入银河系中心附近的”黑洞”时发出的引力辐射脉冲。我们研究一个小粒子落在史瓦西背景（“黑洞”）中的问题，并在高频极限下研究它的光谱。在表述这个问题时，必须提出正确的边界条件：引力辐射不仅逃逸到无穷远，而且消失在黑洞中。利用Regge和惠勒（1957）以及马修斯（1962）给出的张量球谐函数的分解，我们研究了从史瓦西背景几何近似线性扰动的问题。下落粒子贡献了一个δ函数源项（背景史瓦西几何中的测地线运动），它也被分解为张量谐波，每个张量谐波”驱动”相应的微扰谐波。无限远辐射的功率谱是在高频近似下，根据马修斯称为”电”和”磁”的无痕横向张量谐波给出的。
We are concerned with the pulse of gravitational radiation given off when a star falls into a" black hole" near the center of our galaxy. We look at the problem of a small particle falling in a Schwarzschild background (" black hole") and examine its spectrum in the high-frequency limit. In formulating the problem it is essential to pose the correct boundary condition: gravitational radiation not only escaping to infinity but also disappearing down the hole. We have examined the problem in the approximation of linear perturbations from a Schwarzschild background geometry, utilizing the decomposition into the tensor spherical harmonics given by Regge and Wheeler (1957) and by Mathews (1962). The falling particle contributes a δ-function source term (geodesic motion in the background Schwarzschild geometry) which is also decomposed into tensor harmonics, each of which" drives" the corresponding perturbation harmonic. The power spectrum radiated in infinity is given in the high-frequency approximation in terms of the traceless transverse tensor harmonics called" electric" and" magnetic" by Mathews.