Kundt spacetimes as solutions of topologically massive gravity

TL;DR

This paper derives new Kundt solutions in three-dimensional topologically massive gravity, including algebraic types II, III, N, D, with some solutions being previously unknown and characterized by constant scalar invariants.

Contribution

It presents the first known algebraic type II and III Kundt solutions in topologically massive gravity, expanding the solution space with explicit CSI cases and differential equation reductions.

Findings

Type D solutions are spacelike-squashed AdS_3

Type N solutions include known and new AdS pp-waves

Type II and III solutions are newly identified with constant scalar invariants

Abstract

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.