Hamiltonian evolution and quantization for extremal black holes (Q2783435)

The authors compare different approaches to calculate the entropy of a black hole. They restrict to those approaches where the Lorentzian signature of the metric remains; one should mention that other approaches with Wick rotation to the Euclidean signature exist, too. Here, the authors discuss the continuity of the entropy by continuous changes of the black hole's parameters. The non-trivial part of this question arises, when the black hole changes from non-extremal to extremal. Here, the authors give two different Hamiltonian approaches to solve the problem of entropy, and they mention several unsolved problems, e.g., in connection with naked singularities. The appendix explains the notion of an extremal black hole as a space-time, where the \(g_{00}\)-component of the metric has a double root.