Black holes on cylinders are not algebraically special

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  • 12 June 2002
Abstract
We give a Petrov classification for five-dimensional metrics. We give an almost complete classification of Ricci-flat metrics that are static, have an SO(3) isometry group and have Petrov type 22. We use this classification to look for the metric of a black hole on a cylinder, i.e. a black hole with asymptotic geometry four-dimensional Minkowski space times a circle. Although a black string wrapped around the circle and the five-dimensional black hole are both algebraically special, it turns out that the black hole on a cylinder is not.

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