Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
General Relativity and Quantum Cosmology
2009-11-19 v1 High Energy Physics - Theory
Abstract
A d-dimensional spacetime is "axisymmetric" if it possesses an SO(d-2) isometry group whose orbits are (d-3)-spheres. In this paper, algebraically special, axisymmetric solutions of the higher dimensional vacuum Einstein equation (with cosmological constant) are investigated. Necessary and sufficient conditions for static axisymmetric solutions to belong to different algebraic classes are presented. Then general (possibly time-dependent) axisymmetric solutions are discussed. All axisymmetric solutions of algebraic types II, D, III and N are obtained.
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Cite
@article{arxiv.0904.4368,
title = {Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation},
author = {Mahdi Godazgar and Harvey S. Reall},
journal= {arXiv preprint arXiv:0904.4368},
year = {2009}
}
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28 pages