Spin entropy for Kerr black holes

It is known that the entropy for a singular spacetime metric can be calcula ted in the framework of classical field theories by applying Noether's theo rem to stationary solutions of Einstein's field equations, integrating a su itable form on a trapping surface for the singularity. When the Kerr soluti on is considered, two different horizons appear. The physical entropy for t he system is well known to be related to the outer horizon. We investigate here which is the meaning of the entropy calculated (via first principle of black hole thermodynamics) on the inner horizon. We show that this entropy , which was earlier interpreted as a sort of "spin entropy" of the black ho le, admits in fact an interpretation as a quantity associated to a conserve d charge which is related to the rotational degrees of freedom of the syste m.