Properties of Kaluza-Klein Black Holes

We detail numerical methods to compute the geometry of static vacuum blackholes in 6 dimensional gravity compactified on a circle. We calculateproperties of these Kaluza-Klein black holes for varying mass, while keepingthe asymptotic compactification radius fixed. For increasing mass the horizondeforms to a prolate ellipsoid, and the geometry near the horizon and axisdecompactifies. We are able to find solutions with horizon radii approximatelyequal to the asymptotic compactification radius. Having chosen 6-dimensions, wemay compare these solutions to the non-uniform strings compactified on the sameradius of circle found in previous numerical work. We find the black holesachieve larger masses and horizon volumes than the most non-uniform strings.This sheds doubt on whether these solution branches can merge via a topologychanging solution. Further work is required to resolve whether there is amaximum mass for the black holes, or whether the mass can become arbitrarilylarge.Comment: 33 pages, 13 colour figures; v2 minor corrections and some figures beautifie