Kerr-Newman（anti）de Sitter黑洞弯曲时空中的Klein-Gordon-Fock方程
The Klein-Gordon-Fock equation in the curved spacetime of the Kerr-Newman (anti) de Sitter black hole
摘要：
研究了在弯曲的带电旋转Kerr-Newman-（anti）de Sitter黑洞中描述大质量带电标量粒子动力学的Klein-Gordon-Fock（KGF）方程的精确解.在一般情况下的旋转，充电，宇宙黑洞的KGF方程的解与分离变量的方法的结果在Fuchsian微分方程的径向和角的部分，其中包含超过三个有限的奇异性，从而推广Heun微分方程（HE）。对于特定值的物理参数（即质量的标量粒子），这些Fuchsian方程减少到Heun方程和解决方案表示的Heun函数。对于其他参数值，一些额外的奇异点是假奇异点。我们推导出广义Fuchsian方程系数的条件，使得奇点是假点。在这种情况下，Fuchsian方程的精确解原则上可以简化并用Heun函数表示。我们还导出了克尔-纽曼时空中大质量标量（带电）粒子的径向和角度方程的精确解。解析解用合流Heun函数表示。此外，我们推导出的理论参数的约束条件，使解决方案简化，并表示为合流Kummer超几何函数。我们还研究了KN情况下在事件视界附近和远离黑洞区域的径向解。最后，我们构造了几个扩展的解决方案的HE的广义超几何函数的Lauricella-Appell。
英文摘要：
Exact solutions of the Klein-Gordon-Fock (KGF) general relativistic equation that describe the dynamics of a massive, electrically charged scalar particle in the curved spacetime geometry of a charged, rotating Kerr-Newman-(anti) de Sitter black hole are investigated. In the general case of a rotating, charged, cosmological black hole the solution of the KGF equation with the method of separation of variables results in Fuchsian differential equations for the radial and angular parts which contain more than three finite singularities and thereby generalise the Heun differential equations (HE). For particular values of the physical parameters (i.e mass of the scalar particle) these Fuchsian equations reduce to Heun equations and the solutions are expressed in terms of Heun functions. For other values of the parameters some of the extra singular points are false singular points. We derive the conditions on the coefficients of the generalised Fuchsian equation such that a singular point is a false point. In such a case the exact solution of the Fuchsian equation can in principle be simplified and expressed in terms of Heun functions. We also derive the exact solutions of the radial and angular equations for a massive scalar (charged) particle in the Kerr-Newman spacetime. The analytic solutions are expressed in terms of confluent Heun functions. Moreover, we derived the constraints on the parameters of the theory such that the solution simplifies and expressed in terms of confluent Kummer hypergeometric functions. We also investigate the radial solutions in the KN case in the regions near the event horizon and far from the black hole. Finally, we construct several expansions of the solutions of the HE in terms of generalised hypergeometric functions of Lauricella-Appell.
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