Topological Stars and Black Holes.

We study smooth bubble spacetimes in five-dimensional Einstein-Maxwell theory that resemble four-dimensional magnetic black holes upon Kaluza-Klein reduction. We denote them as topological stars since they have topological cycles supported by magnetic flux. They can be macroscopically large compared to the size of the Kaluza-Klein circle and could describe qualitative properties of microstate geometries for astrophysical black holes.