Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations

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In this paper, we study the problem of the nonlinear interaction of impulsive gravitational waves for the Einstein vacuum equations.

• The problem is studied in the context of a characteristic initial value problem with data given on two null hypersurfaces and containing curvature delta singularities.
• We establish an existence and uniqueness result for the spacetime arising from such data and show that the resulting spacetime represents the interaction of two impulsive gravitational waves germinating from the initial singularities.
• In the spacetime, the curvature delta singularities propagate along 3-dimensional null hypersurfaces intersecting to the future of the data.