Schwarzschild时空中的标量场方程

Real Scalar Field in Schwarzschild Spacetime

考察了Schwarzschild时空中标量场方程的数值解(Φ=0).根据该度规下的乌龟坐标x(r)的形式,引进一条正切曲线来近似模拟乌龟坐标x(r)的曲线,从而得到以x为自变量的函数r(x)和势函数V(x),用Maple软件解出标量场方程的数值解并画出波函数的图象.

In the paper, the real scalar field equation in Schwarzschild spacetime is solved numerically （ □Ф = 0）. By generalizing the ＂tortoise＂ coordinate（r）, a ＂tangent＂ approximation is introduced to invert the relationship between r and x so as to exprexs the potential V（x）. By using Maple software, the scalar field equation is solved numerically, and the field amplitude is shown graphically.