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arxiv: 1503.02162 · v1 · submitted 2015-03-07 · 🌀 gr-qc · hep-th· math-ph· math.MP· nlin.SI

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Ricci-flat spacetimes admitting higher rank Killing tensors

Marco Cariglia , Anton Galajinsky
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classification 🌀 gr-qc hep-thmath-phmath.MPnlin.SI
keywords killingricci-flatspacetimestensorsadmitadmittinganti-self-dualapplied
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Ricci-flat spacetimes of signature (2,q) with q=2,3,4 are constructed which admit irreducible Killing tensors of rank-3 or rank-4. The construction relies upon the Eisenhart lift applied to Drach's two-dimensional integrable systems which is followed by the oxidation with respect to free parameters. In four dimensions, some of our solutions are anti-self-dual.

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  1. The Bohlin variant of the Eisenhart lift

    nlin.SI 2026-02 unverdicted novelty 7.0

    The Bohlin variant of the Eisenhart lift embeds Lagrangian systems into timelike geodesics of conformally flat (d+2)-dimensional metrics and yields novel examples of such metrics admitting higher-rank Killing tensors.