Gibbons-Maeda dilaton时空中Klein-Gordon方程的近似解

Gibbons-Maeda dilaton时空中Klein-Gordon方程的近似解
 
摘要：本文从Gibbons-Maeda dilaton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，重点是求解径向方程。本文利用参量变换将径向方程化为类薛定谔方程进行求解，忽略 后可将方程化为合流超几何方程，其解为合流超几何函数。最终我们得出了Gibbons-Maeda dilaton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：Gibbons-Maeda dilaton黑洞；Klein-Gordon方程；近似解。

Approximate solution of Klein-Gordon equation in Gibbons-Maeda dilaton black hole
 
Abstract: In this paper, we study the solution of Klein-Gordon equation in Gibbons-Maeda dilaton 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 function of spherical harmonics. Here we mainly study the solution of radial equation. The radial equation is transformed to Schrodinger-like equation by variable substitution. If neglect  , we can transform the equation to the generalized hypergeometric equation, and its solution is the generalized hypergometric function. Hence, we can get the approximate solution of Klein-Gordon equation in Gibbons-Maeda dilaton black hole. This method is helpful for us to find the way of the solution of scalar field equation.

Key Words: Gibbons-Maeda dilaton black hole; Kein-Gordon equation; approximate solution.
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