Reissner-Nordstrom黑洞背景时空中Klein-Gordon方程的近似解
 
摘要：本文从Reissner-Nordstrom黑洞背景时空中标量波所满足的Klein-Gordon方程出发，利用分离变量法得到了Klein-Gordon方程的角向方程和径向方程。角向方程的解是已知的球谐函数，本文主要对径向方程进行求解。本文采用一系列参量变化和数学方法将径向方程转化为类薛定谔方程进行求解，从而求出了Reissner-Nordstrom黑洞背景时空中Klein-Gordon方程的近似解。这种求解的方法对于寻求标量场方程的解有一定的启发意义。

关键词： Reissner-Nordstrom黑洞；  Klein-Gordon方程 ； 近似解。

The approximate solution of Klein-Gordon equation in Reissner-Nordstrom black hole
 
Abstract：In this paper，we study the solution of Klein-Gordon equation in Reissner-Nordstrom black hole.We can get its angular equation and radial equation by Separation of variables, and the angular equation is a known mathematical function, its solution is in the form of funcfion of spherical harmonics. Here we mainly study the solution of radial equation. The radial equation is transformed to Schrodinger-like equation by variable substitution and mathematical operation.  Hence, we can get the approximate solution of Klein-Gordon equation in Reissner-Nordstrom black hole. This method is helpful for us to find the way of the solution of scalar field equation.

Key Words：Reissner-Nordstrom black hole；Klein-Gordon equation；approximate solution．

.............................