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Axisymmetric metrics in arbitrary dimensions

Christos Charmousis·Ruth Gregory
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Abstract

We consider axially symmetric static metrics in arbitrary dimension, both with and without a cosmological constant. The most obvious such solutions have an SO(n) group of Killing vectors representing the axial symmetry, although one can also consider abelian groups which represent a flat `internal space'. We relate such metrics to lower dimensional dilatonic cosmological metrics with a Liouville potential. We also develop a duality relation between vacuum solutions with internal curvature and those with zero internal curvature but a cosmological constant. This duality relation gives a solution generating technique permitting the mapping of different spacetimes. We give a large class of solutions to the vacuum or cosmological constant spacetimes. We comment on the extension of the C-metric to higher dimensions and provide a novel solution for a braneworld black hole.

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Christos Charmousis, Ruth Gregory. 2004-07-10. Axisymmetric metrics in arbitrary dimensions. https://doi.org/10.1088/0264-9381%2F21%2F2%2F016

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