We study Kerr-Newman black hole in the formalism of isolated horizons using a solution found by Krishnan. The space-time in the neighborhood of a general isolated black hole, Classical and Quantum Gravity, 29, 205 006, 2012.
It establishes the existence of a null tetrad which is tangent to the horizon and parallelly propagated off the horizon along a non-twisting null geodesic congruence. However, the tetrad is not given by Krishnan.
We formulate appropriate initial data and firstly construct such a tetrad in a perturbative way and finally we find also its exact form everywhere in the space-time.