D-dimensional metrics with D-3 symmetries

Hidden symmetry transformations of D-dimensional vacuum metrics with D-3 commuting Killing vectors are studied. We solve directly the Einstein equations in the Maison formulation under additional assumptions. We relate the 4-dimensional Reissner-Nordstr\"om solution to a particular case of the 5-dimensional Gross-Perry metric.Comment: 8 page

SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions

A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres.Comment: 11 page

Generalization Of The Gross-Perry Metrics

A class of SO(n+1) symmetric solutions of the (N+n+1)-dimensional Einstein equations is found. It contains 5-dimensional metrics of Gross and Perry and Millward.Comment: 9 page

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

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.Comment: 28 page