本篇论文主要分四个部分。第一部分是绪论，介绍了一些黑洞的基本性质，和黑洞 热力学的相关知识。 在第二章中，介绍了Rovelli提出的关于黑洞内部体积的一个新的计算方法。这种方法 类似于计算测地线方程的方法。他们选取r = 3 2m的等r类空超曲面，去计算史瓦西黑洞内 部的体积，得出史瓦西黑洞内部的体积是V ∼ 3 √ 3πm 2 v。随后在考虑标量场的情况下用计 算这个体积量子态的方法计算这个体积的熵。得到标量场的熵和贝肯斯坦-霍金熵成比例 关系。随着超前爱丁顿时间v的增加，标量场的熵在增加，贝肯斯坦-霍金熵在减小。并且 标量场的熵增加的量要小于贝肯斯坦-霍金熵减小的量。 在第三章，我们将前人的研究延伸到高维黑洞。首先，用Rovelli的方法计算高维史瓦 西黑洞内部的体积。然后介绍高维斯特藩·玻尔兹曼定律。最后我们计算高维史瓦西黑洞 的熵。我们发现在高维黑洞的情况下，标量场的熵的增加量和贝肯斯坦-霍金熵的减小量 依然成比例。标量场的熵的增加量和贝肯斯坦-霍金熵的减小量的比值和维数有关。这个 比值随着随着维数的增加而减小。 在第四章，我们用前面的方法计算了Lifshitz黑洞标量场的熵。同时我们用Rovelli的 方法分析了Regular黑洞内部的最大体积随各参数的变化。

This paper is constructed in four parts. Chapter 1 is introduction.

We introduce some basic knowledge of black hole and some related knowledge of black hole thermodynamics. In chapter 2, we introduce a new method which was suggested by Rovelli to calculate the interior of black hole. This method is similar to the method to calculate the geodesic equation. They select r-constant hypersurface with r = 3 2m to calculate the volume of the interior of Schwarzschild black hole. They found that the volume the interior of Schwarzschild black hole is V ∼ 3 √ 3πm 2 v.

Then using the method of counting the number of quantum states in the volume to calculate the entropy in the case of scalar field. Then we found that the entropy of scalar field is proportional to the Beikenstein-Hawking entropy. With the increase of advanced time v, the entropy of scalar field is increase and the Beikenstein-Hawking entropy is decrease. The amount of the entropy of scalar field is increases is smaller than the amount of the Beikenstein-Hawking entropy decreases.

In chapter 3, we extend their research to high-dimensional black hole. First, using Rovelli’s method to calculate the interior volume of high-dimensional Schwarzschild black hole. And then we introduce the high-dimensional Stefan-Boltzmann law. Finally we calculate the entropy in the high-dimensional Schwarzschild black hole. We find that the entropy of scalar field is also proportional to the Bekenstein-Hawking entropy.The ratio between the incerase of the entropy of scalar field and the decrease of the Bekenstein-Hawking entropy is related to the spacetime dimension, which will decrease with the increase of dimension.

In chapter 4, we use the previous method to calculate the entropy of the scalar field of the Lifshitz black hole.Meanwhile, we use Rovelli’s method to analyze the maximum volume inside the Regular black hole with various parameters.