Topologically massive planar universes with constant twist (Q1096206)

This paper is concerned with ``topologically massive Einstein equations in three dimensions'' \[ (*)\quad R_{ik}+(1/m)C_{ik}=0 \] where \(R_{ik}\) denotes the Ricci tensor, and \(C_{ik}\) denotes the three dimensional Weyl tensor. (The field equation (*) can be derived from ``Einstein-Hilbert-action \(+\) Chern-Simons-action''.) The solution to (*), which admits a timelike Killing field K, are investigated. In particular, it is shown that: (i) if the ``twist'' \((=rotation)\) of K vanishes, then the metric has to be flat; (ii) if the twist of K is constant, then the spatial part of the metric has constant curvature.