Abstract
We investigate geometry of an axially symmetric extremal isolated horizon and prove its uniqueness. Constraints on the geometry are shown and solved explicitly in the extremal case.
It yields a unique 5-parametric solution. Subsequently, a similar result is derived from the Plebanski-Demianski metric.
In some special cases of vanishing parameters of the Plebanski-Demianski metric, identification of both solutions is possible. Hence, we oer a physical interpretation of the parameters of the extremal isolated horizon.