Gravitational Degrees of Freedom and the Initial-Value Problem

It is shown that for every spacelike three-geometry there exists a symmetric tensor that is (1) defined locally using only the three-metric and its derivatives, (2) conformally invariant, (3) traceless, and (4) covariantly divergence free ("transverse"). As a result, the arbitrarily specifiable (unconstrained) initial-value data in the Einstein initial-value problem for gravity can be completely characterized by a pair of symmetric, transverse, traceless tensors.