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Gibbons-Maeda dilaton時空中Klein-Gordon方程的近似解
Gibbons-Maeda dilaton時空中Klein-Gordon方程的近似解
摘要：本文從Gibbons-Maeda dilaton黑洞背景時空中標量波所滿足的Klein-Gordon方程出發，利用分離變量法得到了Klein-Gordon方程的角向方程和徑向方程。角向方程的解是已知的球諧函數，重點是求解徑向方程。本文利用參量變換將徑向方程化為類薛定諤方程進行求解，忽略 后可將方程化為合流超幾何方程，其解為合流超幾何函數。最終我們得出了Gibbons-Maeda dilaton黑洞背景時空中Klein-Gordon方程的近似解。這種求解的方法對于尋求標量場方程的解有1定的啟發意義。
關鍵詞：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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