Axisymmetric metrics in arbitrary dimensions

TL;DR

This paper explores axially symmetric static metrics in any dimension, establishing dualities and solution-generating techniques, and introduces new solutions including a higher-dimensional C-metric extension and a braneworld black hole.

Contribution

It develops a duality relation and solution-generating method for higher-dimensional axially symmetric metrics, including new solutions like a braneworld black hole.

Findings

Established duality between internal curvature and cosmological constant solutions.

Developed a solution-generating technique for various spacetimes.

Provided a novel higher-dimensional C-metric and braneworld black hole solution.

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.