We focus on main differences between stationary frames in the Kerr geometry and the Kerr-de Sitter geometry. This comparison leads to new solutions on the symmetry axis and in the equatorial plane. This solution can clearly be described and physically interpreted. The most interesting is the case of freely falling stationary observers on the symmetry axis. We found a solution which can show that rotating supermassive black holes (not necessary fast rotating) could differ in a certain way from the same bodies for which the present value of the cosmological constant is not included. We show that an interesting family of "freely falling stationary observers" can be found.