HOMOGENEOUS SOLUTIONS TO TOPOLOGICALLY MASSIVE GRAVITY

The classical vacuum equations of topologically massive gravity are investigated for the case of homogeneous spacetimes. For the Euclidean case, all homogeneous solutions are classified using the Bianchi classification for three dimensional Lie algebras, and it is found that only one family of solutions exists. In the Lorentzian case, a classification of all solutions with simply transitive isometry group is presented, and various families of non-trivial solutions are found. The solutions presented incorporate the cases found in previous work on topologically massive gravity by Percacci, Sodano and Vuorio. © 1990.