黑洞作为广义相对论的一个重要预言 ，在近些年的研究中越来越占有重要的地位。而无自旋的史瓦西黑洞和有自旋的克尔黑洞是两种比较典型的黑洞，并且它们是唯有的存在解析解的黑洞，即从Einstein方程R_ab-1/2 Rg_ab=8πGT_ab推出它的解析度规。本文主要研究了在这两种度规下的标量场方程的行为，找到了它的一个不变量即能量模。本文从求解1+1维简单的史瓦西黑洞的能量模出发，利用kerr-schild坐标系，解出了1+3维克尔黑洞的能量模。并且带入黑洞外侧的现实空间对结果分别进行了验证。

Black hole is a significant inference of the general theory of relativity. The theatrical study on the black hole played a very important role in the physics research in the last decade. Schwarzschild black hole, which is uncharged and no spins, is one of the most important models, as well as the Kerr black hole, which is charged and spins. Both of them have analytic solutions, which means that we can get the analytic metrics from Einstein equation, R_ab-1/2 Rg_ab=8πGT_ab. In this paper, the analytic metrics will be used to describe the behavior of scalar quantity equation, and help us to find the unchanging quantity of it, the energy mode. Firstly, we will calculate the energy mode of the most simply condition, the 1+1 dimension Schwarzschild black hole. Then the Kerr-Schild coordinate will be used to calculate the energy mode of the 1+3 dimension Kerr black hole. After that, the results will be proved by fitting them in the conditions outside the black hole.