Kerr black hole in the formalism of isolated horizons

We revise the work of Scholtz, Flandera and G\"urlebeck [Kerr-Newman black hole in the formalism of isolated horizons, Phys. Rev. D 96, 064024 (2017)]. We cast the Kerr metric explicitly in the form suitable for the framework of isolated horizons. We proceed in a geometrical fashion and are capable to provide the results in a compact closed manner, without any unevaluated integrals. We also discuss the uniqueness and drawbacks of this construction. We suggest a new vector field to generate the null geodesic foliation.