Algebraically special axisymmetric solutions of the higher-dimensional vacuum Einstein equation

Understand

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.