Reissner-Nordstrom黑洞背景时空中Klein-Gordon方程的近似解

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1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1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．

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