Exact solutions of topologically massive gravity
Year: 2009
Type: preprint
Abstract: 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. General techniques and classifications of solutions are reviewed. We show that biaxially squashed AdS3 solutions follow from assuming algebraic type D curvature for which the one-dimensional eigenspace of the traceless Ricci tensor is aligned with a Killing vector. We find the general Kundt solutions: spacetimes admitting an expansion-free geodesic null congruence. These provide the first examples of solutions with algebraic types III and II. We find that a Kundt solution of algebraic type D must be biaxial spacelike-squashed AdS3. We present explicitly the Kundt solutions for which all scalar polynomial curvature invariants are constant, and find that all Kundt solutions with algebraic types D, N and III have this property. These constant scalar invariant Kundt solutions are deformations of round or biaxial spacelike-squashed AdS3, and include AdS pp-waves. We also provide a comprehensive review of the literature, showing that most known solutions are locally equivalent to biaxially squashed AdS3 or AdS pp-waves. Contents
Source: arXiv (Cornell University)
Authors: David D. K. Chow, C.N. Pope, Ergin Sezgin
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2967600324