Intrinsic topological structure of entropy of Kerr black holes

Abstract

In the light of φ-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 Gauss-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 bove-mentioned methods.