THE CHARACTERISTIC GLUING PROBLEM FOR THE EINSTEIN EQUATIONS AND APPLICATIONS

In this paper, we introduce the characteristic gluing problem for the Einstein vacuum equations. We present a codimension-10 gluing construction for characteristic initial data which are close to the Minkowski data and we show that the 10-dimensional obstruction space consists of gauge-invariant charges which are conserved by the linearized null constraint equations. By relating these 10 charges to the ADM energy, linear momentum, angular momentum, and the center of mass, we prove that asymptotically flat data can be characteristically glued (including the 10 charges) to the data of a suitably chosen Kerr spacetime, obtaining as a corollary an alternative proof of the Corvino-Schoen spacelike gluing construction. Moreover, we derive a localized version of our construction where the given data restricted on an angular sector is characteristically glued to the Minkowski data restricted on another angular sector. As a corollary, we obtain an alternative proof of the Carlotto-Schoen localized spacelike gluing construction. Our method yields no loss of decay in the transition region, resolving an open problem. We also discuss a number of other applications.