借助 Zerilli 变量，球对称黑洞微扰的线性化 Einstein 场方程在偶宇称模式下可以约化成一个简单的二阶波动方程即主方程的形式，求解该方程即可得到描述扰动衰减的准正规频率. 但当我们试图从Zerilli变量重构微扰度规时，需要对其做一次额外的时间积分和大量微分操作从而构成高阶微扰研究的计算负担；同时将高阶微扰约化为带有源项的Zerilli方程时，由于源项是低阶微扰度规分量的二次函数，额外的微积分操作将造成源函数的表达式很难被解析地写出. 本文从线性化Einstein场方程出发，直接选择微扰度规分量为主变量，导出了球对称黑洞偶宇称微扰的时间二次—空间三次偏微分方程，求解了该方程并将所得准正规频率跟通过Zerilli变量计算的结果进行了比较，确立了两种计算思路的等效性，从而为高阶微扰的计算提供了更具优势的准备.

With the help of Zerilli variable，the linearised Einstein equation can be reduced to a simple second order wave equation，from which we solve the quasi-normal frequency routinely. However，if we try to calculate the perturbed metric them selves，we need to do one extra time integration and many spatial differentials on the power serial form master variables. This forms heavy burden for the second order perturbation calculation. This paper takes the perturbation metric components themselves (either one of the three) as master variables and derives out their differential equations directly，which are spatially differentiated three times and temporarily differentiated twice. We solve this equation by the usual power serial method and get quasi-normal frequencies coincident with those solved out from Zerilli equation，thus we establish an equivalences between the two methods and making much advantageous preparation for higher order perturbations calculation.