TITLE: Open problems in General Relativity
QUESTION [169 upvotes]: I would like to know if there are some open mathematical problems in General Relativity, that are important from the point of view of Physics. 
Is there something that still needs to be justified mathematically in order to have solid foundations?

REPLY [14 votes]: There are some problems related to initial data, such as if gravity can be "insulated", or if there exist generic set of spacetimes which do not admit CMC spacelike hypersurface.