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On stationary metrics in five dimensions

Pieter-Jan De Smet
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Abstract

It is well-known that the Kerr-metric (rotating black hole in four dimensions) has Petrov type D. We prove a similar property in five dimensions. The Myers-Perry metric (rotating black hole in five dimensions) with one non-zero angular momentum has Petrov type \underline{22}. Conversely, we show that the Myers-Perry solution is unique within a certain restricted class of metrics of Petrov type \underline{22}.

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Pieter-Jan De Smet. 2003-06-06. On stationary metrics in five dimensions. https://arxiv.org/abs/gr-qc/0306026

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