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We extend Dain's construction of a geometric invariant characterising staticinitial data sets for the vacuum Einstein field equations to situations with anon-vanishing extrinsic curvature. This invariant gives a measure of how muchthe initial data sets deviates from stationarity. In particular, it vanishes ifand only if the initial data set is stationary. Thus, the invariant provides aquantification of the amount of gravitational radiation contained in theinitial data set.

Dain's invariant on non-time symmetric initial data sets