In their book on the nonlinear stability of Minkowski spacetime, Christodoulou and Klainerman state (p. 15, in the print version): "We recall that the space of dynamical degrees of freedom of the gravitational field at a point can be identified with $\hat{S}_2(\Pi)$, the space of trace-free symmetric 2-covariant tensors on the 2-plane $\Pi$."
I'm completely lost as to what this sentence means; any references would be appreciated. For instance, is the gravitational field in this case the metric $g_{\mu\nu}$? Or the curvature tensor? The metric is not trace-free, so I don't see exactly how the former could be the case.