Properties of Kaluza-Klein black holes

We detail numerical methods to compute the geometry of static vacuum black holes in 6 dimensional gravity compactified on a circle. We calculate properties of these Kaluza-Klein black holes for varying mass, while keeping the asymptotic compactification radius fixed. For increasing mass the horizon deforms to a prolate ellipsoid, and the geometry near the horizon and axis decompactifies. We are able to find solutions with horizon radii approximately equal to the asymptotic compactification radius. Having chosen 6-dimensions, we may compare these solutions to the non-uniform strings compactified on the same radius of circle found in previous numerical work. We find the black holes achieve larger masses and horizon volumes than the most non-uniform strings. This sheds doubt on whether these solution branches can merge via a topology changing solution. Further work is required to resolve whether there is a maximum mass for the black holes, or whether the mass can become arbitrarily large.