Abstract
In the light of topological current and the relationship betweenthe entropy and the Euler characteristic, thetopological aspects of entropy and phase transition of Kerr blackholes are studied. From Gauss–Bonnet–Chern theorem, it isshown that the entropy of Kerr black holes is determined by thesingularities of the Killing vector field of spacetime. Bycalculating the Hopf indices and Brouwer degrees of the Killingvector field at the singularities, the entropy S = A/4 fornonextreme Kerr black holes and S = 0 for extreme ones areobtained, respectively. It is also discussed that, with the changeof the ratio of mass to angular momentum for unit mass, the Eulercharacteristic and the entropy of Kerr black holes will changediscontinuously when the singularities on Cauchy horizon mergewith the singularities on event horizon, which will lead to thefirst-order phase transition of Kerr black holes.
Published Version
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