标题： 无源带电大质量标量场方程在Kerr-Newman背景下的精确解 显示英文标题

标题： Exact Solutions to Sourceless Charged Massive Scalar Field Equation on Kerr-Newman Background

摘要： 源无质量复标量场方程在Kerr-Newman黑洞背景下的分离径向部分被证明是一个虚数阶的广义自旋加权球面波方程。 而分离的角向部分是一个普通的球面波方程。 给出了非极端情况下径向方程的积分形式和幂级数展开的一般精确解，以及几种具有物理兴趣的特殊解。 在极端情况下，简要研究了径向方程的幂级数解。 讨论了两种情况下一般解的幂级数展开系数之间的递推关系以及径向方程之间的联系。 显示英文摘要

摘要： The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated angular part is an ordinary spheroidal wave equation. General exact solutions in integral forms and in power series expansion as well as several special solutions with physical interest are given for the radial equation in the non-extreme case. In the extreme case, power series solution to the radial equation is briefly studied. Recurrence relations between coefficients in power series expansion of general solutions and connection between the radial equation are discussed in both cases.