Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation

Abstract

We study relative motion of nearby test particles in Topologically Massive Gravity (TMG) in three spacetime dimensions, using the equation of geodesic deviation. We show that, in a suitable reference frame, the influence of any gravitational field can be decomposed into transverse, longitudinal, and Newtonian components, which are directly related to the Cotton scalars of the Newman-Penrose-type. In particular, we prove that Cotton type N spacetimes exhibit a purely transverse gravitational effect on test particles, and can thus be reasonably interpreted as specific gravitational waves with a single polarization mode in TMG. The influence of the cosmological constant manifests itself as an isotropic effect. We also discuss the physical interpretation of spacetimes of specific algebraic types, as well as the influence of various matter fields, namely pure radiation, perfect fluid, and electromagnetic field. As an example, we provide an explicit analysis of TN-waves and pp-waves in three-dimensional TMG.

26 pages, 2 figures, 1 table

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