For non-extremal Reissner-Nordström and Kerr black holes both horizon regularity and the Chern-Gauss-Bonnet theorem fix the Euclidean time period and reproduce the Bekenstein-Hawking entropy, while for extremal black holes the period and hence the entropy are not fixed by either method.
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From Nonextremal to Extremal: Entropy of Reissner-Nordstr\"om and Kerr black holes Revisited
For non-extremal Reissner-Nordström and Kerr black holes both horizon regularity and the Chern-Gauss-Bonnet theorem fix the Euclidean time period and reproduce the Bekenstein-Hawking entropy, while for extremal black holes the period and hence the entropy are not fixed by either method.