Axisymmetric metrics in arbitrary dimensions

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.