Uniqueness theorem for Kaluza-Klein black holes in five-dimensional minimal supergravity

We show a uniqueness theorem for Kaluza-Klein black holes in the bosonic sector of five-dimensional minimal supergravity. More precisely, under the assumptions of the existence of two commuting axial isometries and a nondegenerate connected event horizon of the cross-section topology S3, or lens space, we prove that a stationary charged rotating Kaluza-Klein black hole in five-dimensional minimal supergravity is uniquely characterized by its mass, two independent angular momenta, electric charge, magnetic flux, and nut charge, provided that there exists neither a nut nor a bolt (a bubble) in the domain of outer communication. We also show that under the assumptions of the same symmetry, same asymptotics, and the horizon cross section of S1xS2, a black ring within the same theory--if it exists--is uniquely determined by its dipole charge and rod intervals besides the charges and magnetic flux.