Dominant energy condition: From initial data sets to spacetimes

The dominant energy condition (DEC) is a curvature condition for Lorentzian manifolds that is of great physical importance. The same name also denotes a condition for initial data sets -- the pairs of induced metric and second fundamental form on spacelike hypersurfaces -- that is induced by the spacetime DEC. In this talk, I want to elaborate on the connection between those two conditions and illustrate how the study of the initial data DEC can lead to consequences about DEC spacetimes.