just throwing a query out to the Math community. I'm about to embark on a master's in Gravitation, Cosmology and General Relativity and was looking for possible subjects to start researching. My main interests are in the geometrical side of things (i.e. differential geometry or anything focused on geometry) but am open to interesting, subtle and exciting topics.
So far I've been looking at Carter-Penrose hypersurfaces, matching/junction conditions for given metrics; otherwise I'm not having much luck in topics which could be deemed "original" or "new".
If anybody has any advice on research topics or books/papers I could/should be reading, it would be immensely appreciated!