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We generalise uniqueness theorems for non-extremal black holes with threemutually independent Killing vector fields in five-dimensional minimalsupergravity in order to account for the existence of non-trivial 2-cycles inthe domain of outer communication. The black hole space-times we consider maycontain multiple disconnected horizons and be asymptotically flat orasymptotically Kaluza-Klein. We show that in order to uniquely specify theblack hole space-time, besides providing its domain structure and a set ofasymptotic and local charges, it is necessary to measure the magnetic fluxesthat support the 2-cycles as well as fluxes in the two semi-infinite rotationplanes of the domain diagram.

Uniqueness of Black Holes with Bubbles in Minimal Supergravity