Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation
Mahdi Godazgar, Harvey S. Reall
TL;DR
This paper classifies and derives algebraically special axisymmetric solutions to the higher-dimensional vacuum Einstein equations, including static and dynamic cases, covering types II, D, III, and N.
Contribution
It provides necessary and sufficient conditions for static solutions and explicitly constructs all axisymmetric solutions of algebraic types II, D, III, and N in higher dimensions.
Findings
Classified static axisymmetric solutions by algebraic type.
Derived all solutions of types II, D, III, N.
Established conditions for solutions to belong to specific algebraic classes.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.