In a series of work, Aretakis, Czimek, and Rodnianski have studied the gluing of two sets of initial data to the Einstein equations along a null surface. By solving the linearized gluing problem around Minkowski and using the implicit function theorem, they have shown that two sets of C2 “sphere data” sufficiently close to Minkowski can be glued together along a null surface up to a ten dimensional obstruction space. In this talk, I will present a generalisation of this result to (i) higher dimensions, (ii) include the cosmological constant and (iii) the gluing of higher regularity Ck data. Based on joint work with Piotr Chrusciel and Finnian Gray arXiv:2401.04442 [gr-qc]
