Simultaneous baldness and cosmic baldness and Kottler spacetime

The uniqueness of the Kottler/Schwarzschild-de Sitter solution of the vacuum Einstein equations with positive cosmological constant is discussed and certain putative alternatives are shown to either solve different equations or to be the KSdS solution in disguise. A simultaneous no-hair and cosmic no-hair theorem for the KSdS geometry in the presence of an imperfect fluid is proved.