We interpret the cosmological constant as the energy of the vacuum, and under a minimum amount of assumptions, we show that it is deformed in the vicinity of a black hole. This leads us to reexamine the Kerr-de Sitter solution. We provide a new solution, simpler and geometrically richer, which shows the impact of the rotation in form of a warped curvature. We carry out a detailed and exact study on the new black hole solution, and we conclude with a conjecture regarding the possible impact of our results on alternative theories.