Gravitational field of a Schwarzschild black hole and a rotating mass ring
Gravitational field of a Schwarzschild black hole and a rotating mass ring
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史瓦西黑洞和旋转质量环的引力场
DOI：
10.1103/physrevd.90.044043
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发表时间：
2014
影响因子：
5
通讯作者：
Yasumichi Sano and Hideyuki Tagoshi
中科院分区：
文献类型：
--
作者：
M.Harada;S.Matsuzaki;K.Yamawaki;江尻信司;小澤秀敏;Yasumichi Sano and Hideyuki Tagoshi
本文利用Newman-Penrose形式讨论了Kerr黑洞的线性微扰，微扰后的Weyl标量可由Teukolsky方程得到。为了得到其他外尔标量和微扰度规，Chrzanowski和Cohen和Kegeles提出了一种形式，通过赫兹势在辐射规范中构造这些量。作为用这种形式构造扰动引力场的一个简单例子，我们考虑了围绕史瓦西黑洞旋转的圆环产生的引力场。在Chrzanowski，Cohen和Kegeles的方法中，度规是通过赫兹势在辐射规范中构造的，赫兹势是从Teukolsky方程的解获得的。由于Teukolsky方程的解和是自旋为2的量，所以赫兹势被确定到它的双极模和偶极模。如果没有这些低模，构造的度规标量和Newman-Penrose Weyl标量在环半径处的球面上有非物理的跳跃。我们发现，当我们把角动量微扰加到赫兹势上时，外尔标量虚部的跳跃被抵消了。最后，通过加入质量微扰和选取与规范自由度有关的参数，得到了除环外赤道面上外光滑的微扰引力场。讨论了这些结果对辐射规范中点粒子引力自作用力计算问题的意义。
The linear perturbation of the Kerr black hole has been discussed by using the Newman-Penrose formalism, and the perturbed Weyl scalars,andcan be obtained from the Teukolsky equation. In order to obtain the other Weyl scalars and the perturbed metric, a formalism was proposed by Chrzanowski and by Cohen and Kegeles to construct these quantities in a radiation gauge via the Hertz potential. As a simple example of the construction of the perturbed gravitational field with this formalism, we consider the gravitational field produced by a rotating circular ring around a Schwarzschild black hole. In the method by Chrzanowski, Cohen, and Kegeles, the metric is constructed in a radiation gauge via the Hertz potential, which is obtained from the solution of the Teukolsky equation. Since the solutionsandof the Teukolsky equations are spin-2 quantities, the Hertz potential is determined up to its monopole and dipole modes. Without these lower modes, the constructed metric and Newman-Penrose Weyl scalars have unphysical jumps on the spherical surface at the radius of the ring. We find that the jumps of the imaginary parts of the Weyl scalars are cancelled when we add the angular momentum perturbation to the Hertz potential. Finally, by adding the mass perturbation and choosing the parameters which are related to the gauge freedom, we obtain the perturbed gravitational field which is smooth except on the equatorial plane outside the ring. We discuss the implication of these results to the problem of the computation of the gravitational self-force to the point particles in a radiation gauge.