This may help: Given a spacetime manifold with metric and no matter that is flat an infinity, you can mathematically define the amount of curvature in it, which

This may help: Given a spacetime manifold with metric and no matter that is flat an infinity, you can mathematically define the amount of curvature in it, which is directly related to how much energy in conventional forms (say, kinetic) that could be transferred to matter. Just as two merging black holes can emit gravitational waves, which have energy in this sense and escape to infinity, gravitational waves coming in from infinity can collapse into a black hole where no black hole previously existed.