中文摘要：

根据印射在熵和 Euler 特征之间的方法和关系的蠁 - ，克尔黑人洞的熵的内在的拓扑的结构被学习。从 Gauss-Bonnet-Chem 定理，克尔黑人洞的熵被 spacetime 的杀死的向量领域的奇特决定，这被显示出。这些奇特自然地带拓扑的数字， Hopf 索引和 Brouwer 学位，它能也被看作克尔黑人洞的熵的拓扑的量子化。为非极端的克尔黑人洞的特定的结果 S=A/4 和为极端的 S=0 被使用提及 bove 的方法独立地计算。关键词熵-克尔黑人洞- Euler 特征-杀死向量地 PACS 2001 04.70 .Dy - 04.20 .G2 - 04.62 .+V 工程由国家天赋支持了中国(资助号码 10447125 )的科学基础，科技的上海市政的委员会的科学基础(资助Nos. 04dz05905 ， 04ZR14059 )

英文摘要：

In the light of Ф-mapping method and the relationship between entropy and the Euler characteristic, the intrinsic topological structure of entropy of Kerr black holes is studied. From the Ganss-Bonnet-Chem theorem, it is shown that the entropy of Kerr black hole is determined by singularities of the Killing vector field of spacetime. These singularities naturally carry topological numbers, Hopf indices and Brouwer degrees, which can also be viewed as topological quantization of entropy of Kerr black holes. Specific results S = A/4 for non-extreme Kerr black holes and S = 0 for extreme ones are calculated independently by using the above-mentioned methods.