Charged black holes in a five-dimensional Kaluza-Klein universe

We examine an exact solution which represents a charged black hole in a Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The spacetime approaches to the five-dimensional Kasner solution that describes a universe with the expanding three-dimensional space and the shrinking extra dimension in the far region. The metric is continuous but not smooth at the black hole horizon. There appears a mild curvature singularity that a free-fall observer can traverse the horizon. The horizon is a squashed three-sphere with a constant size, and the metric is approximately static near the horizon.