We analyze the properties of the black hole surface gravity by using an alternative approach based upon the use of light surfaces that are represented by certain characteristic frequencies. To this end, we rewrite the Kerr line element in terms of the characteristic frequencies, which allows us to obtain copies of the Kerr geometries (black hole-clusters) as the parameters vary. In particular, we replace the spin parameter a = J/M with the corresponding characteristic frequencies so that the line element describes only black holes. This new representation is particularly adapted to analyze how the surface gravity behaves as the black hole passes from one v state to another. It turns out that the spins a = v3/2M and a = 1/v 2 M for black holes and a/M = v9/8 for naked singularities are of particular relevance for the analysis of the surface gravity properties.