Gluing Initial Data Sets for General Relativity

Piotr T. Chruściel, James Isenberg, Daniel Pollack
2004 Physical Review Letters  
We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Secondly, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this
more » ... . Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.
doi:10.1103/physrevlett.93.081101 pmid:15447167 fatcat:xjhwmmzzebax3gw7mxkfkvprvq