Further results on non-diagonal: Bianchi type III vacuum metrics

Details Further results on non-diagonal: Bianchi type III vacuum metrics Further results on non-diagonal: Bianchi type III vacuum metrics

Feb 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012gregr.tmp...24v&link_type=abstract

General Relativity and Gravitation, Online First

Physics

Bianchi Iii Vacuum Metric, Hyperkähler Metrics, Killing Tensors

Scientific paper

We present the derivation, for these vacuum metrics, of the Painlevé VI equation first obtained by Christodoulakis and Terzis, from the field equations for both minkowskian and euclidean signatures. This allows to give the precise connection with some old results due to Kinnersley. The hyperkähler metrics are shown to belong to the Multi-Centre class and for the cases exhibiting an integrable geodesic flow the relevant Killing tensors are given. We conclude by the proof that for the Bianchi B family, excluding type III, there are no hyperkähler metrics.

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