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Black holes on cylinders are not algebraically special

Pieter-Jan De Smet
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Abstract

We give a Petrov classification for five-dimensional metrics. We classify 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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Pieter-Jan De Smet. 2003-02-18. Black holes on cylinders are not algebraically special. https://doi.org/10.1088/0264-9381%2F19%2F19%2F307

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