Speaker
Description
Gravitational fields are typically described in terms of local curvature, but the physical interpretation of curvature is not immediately evident. This motivates the study of the motion of test particles, whose relative acceleration is governed, in the simplest approximation, by the equation of geodesic deviation.
In this talk, we apply this concept within topologically massive gravity, a three-dimensional gravity theory with a dynamical degree of freedom. We construct a coordinate-independent description of curvature using invariants of the Cotton tensor. We then demonstrate a natural decomposition of the gravitational field into transverse, longitudinal, and Newtonian components, each characterized by its effects on test particles as described by the geodesic deviation equation.
Relating Cotton invariants to the algebraic classification of spacetimes, we construct an associated interpretation frame. We show that in this frame, type N spacetimes exhibit purely transverse behaviour with a single polarization mode. Additionally, we analyse the effect of specific matter fields on test particle motion and provide the interpretation of pp-wave spacetimes by explicitly solving the equation of geodesic deviation.