Kundt spacetimes as solutions of topologically massive gravity

We obtain new solutions of topologically massive gravity. We find the general Kundt solutions, which in three dimensions are spacetimes admitting an expansion-free null geodesic congruence. The solutions are generically of algebraic type II, but special cases are types III, N or D. Those of type D are the known spacelike-squashed AdS_3 solutions, and of type N are the known AdS pp-waves or new solutions. Those of types II and III are the first known solutions of these algebraic types. We present explicitly the Kundt solutions that are CSI spacetimes, for which all scalar polynomial curvature invariants are constant, whereas for the general case we reduce the field equations to a series of ordinary differential equations. The CSI solutions of types II and III are deformations of spacelike-squashed AdS_3 and the round AdS_3, respectively.Comment: 30 pages. This material has come from splitting v1 of arXiv:0906.3559 into 2 separate papers. v2: minor changes

Witten-Nester Energy in Topologically Massive Gravity

We formulate topologically massive supergravity with cosmological constant in the first order formalism, and construct the Noether supercurrent and superpotential associated with its local supersymmetry. Using these results, we construct in ordinary topologically massive gravity the Witten-Nester integral for conserved charges containing spinors which satisfy a generalized version of Witten equation on the initial value surface. We show that the Witten-Nester charge, represented as an integral over the boundary of the initial value surface produces the Abbott-Deser-Tekin energy for asymptotically anti de Sitter spacetimes. We consider all values of the Chern-Simons coupling constant, including the critical value known as the chiral point, and study the cases of standard Brown-Henneaux boundary conditions, as well as their weaker version that allow a slower fall-off. Studying the Witten-Nester energy as a bulk integral over the initial value surface instead, we find a bound on the energy, and through it the sufficient condition for the positivity of the energy. In particular, we find that spacetimes of Petrov type N that admit globally well defined solutions of the generalized Witten equation have positive energy.Comment: 43 page

Classification of solutions in topologically massive gravity

We study exact solutions of three-dimensional gravity with a cosmological constant and a gravitational Chern-Simons term: the theory known as topologically massive gravity. After reviewing the algebraic classification, we show that if a solution has curvature of algebraic type D, then it is biaxially squashed AdS_3. Applying the classification, we provide a comprehensive review of the literature, showing that most known solutions are locally equivalent to biaxially squashed AdS_3 or to AdS pp-waves.Comment: 39 pages. v1 split into 2 separate papers. This version is the first of the two, containing the classification of solutions, with a strengthening of the type D result. The material on Kundt solutions now appears in the second paper arXiv:0912.3438. v3: minor changes