The Petrov and Kaigorodov-Ozsv\'ath Solutions: Spacetime as a Group Manifold

Understand

The Petrov solution (for $\Lambda=0$) and the Kaigorodov-Ozsv\'ath solution (for $\Lambda<0$) provide examples of vacuum solutions of the Einstein equations with simply-transitive isometry groups.

• We calculate the boundary stress-tensor for the Kaigorodov-Ozsv\'ath solution in the context of the adS/CFT correspondence.
• By giving a matrix representation of the Killing algebra of the Petrov solution, we determine left-invariant one-forms on the group.
• The algebra is shown to admit a two-parameter family of linear deformations a special case of which gives the algebra of the Kaigorodov-Ozsv\'ath solution.