arXiv 0909.48232009-09-26gr-qc

静态对称均匀时空的微扰方程

The perturbation equation of a static symmetrical homogeneous space-time

Jose L. Martinez-Morales

备注：: 38 pages

摘要：

在静态对称均匀时空的微扰方程没有显式解的情况下，我们所能做的最好的工作是构造一个{ \it准}变换。在此框架下，我们解决了扰动方程的初始数据和一些结果。在远离偶数空间维$N$黑洞视界的地方，无质量场在时空中衰变为${r^l} {{(-{r^2}+{t^2})}^{\frac{1-N}{2}-l}}$，其中$l$是球的调和数。发现了超黑洞中粒子的能量和动量与质量的关系，并给出了超球上Schwarzschild-Tangherlini度规下Klein-Gordon方程的一个解.计算了Schwarzschild坐标系下Klein-Gordon方程的格林函数。该函数是球的谐波模式的总和。第一项是能量谱和粒子动量的双重积分。在远离视界的地方，二重积分近似为在由自由粒子的能量和动量关系定义的直线上的积分。从这里，汤川的潜力推导出来。最后，推导出线性摄动方程并精确求解。

英文摘要：

In absence of explicit solutions of the perturbation equation of a static symmetrical homogeneous space-time, the best we can do is to construct a {\it quasi-}transformation. In this framework, we solve the perturbation equation with initial data and a number of results are derived. Far from the horizon of a black hole of even space dimension $N$, a mass-less field decays as ${r^l} {{(-{r^2}+{t^2})}^{\frac{1-N}{2}-l}}$ in space-time, where $l$ is a harmonic number of the sphere. A relation of energy and momentum of a particle with mass in a hyper black hole is discovered and a solution to the equation of Klein-Gordon in the metric of Schwarzschild-Tangherlini with initial data on the hypersphere is proposed. Also, the Green's function of the Klein-Gordon equation in Schwarzschild coordinates is calculated. This function is a sum on the harmonic modes of the sphere. The first term is a double integration on the spectrum of energy and the momentum of the particle. Far from the horizon, the double integration is approximated by an integration on a line defined by the relation of energy and momentum of a free particle. From here, the potential of Yukawa is derived. Finally, the linear perturbation equations are derived and solved exactly.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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