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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!

Thanks! MKF

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    $\begingroup$ 1) Look at the list of faculty that do general relativity at your school. 2) Email those who you find interesting in terms of research interests. $\endgroup$ – Alex R. Jul 8 '15 at 19:58
  • $\begingroup$ Have you checked out The Large Scale Structure of Space-Time by Hawking and Ellis? A real mathematical physics jawbreaker. Cheers! $\endgroup$ – Robert Lewis Jul 8 '15 at 20:00
  • $\begingroup$ Wicked! looks really good; will have a read. This is exactly the kind of thing I was looking for; Thanks! $\endgroup$ – MKF Jul 8 '15 at 20:03
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Not sure if this is exactly what you're looking for but here's some papers from the last few years on topics of interest for mathematicians doing relativity:

  • "Hawing's local rigidity theorem without analyticity" by S. Alexakis, A. Ionescu and S. Klainerman

  • "The red-shift effect and radiation decay on black hole spacetimes" by M. Dafermos and I. Rodnianski

  • "The inverse mean curvature flow and the Riemannian Penrose inequality" by G. Huisken and T. Ilmanen

  • "A fully anisotropic mechanism for formation of trapped surfaces in vacuum" by S. Klainerman, J. Luk and I. Rodnianski

  • "Isometric embeddings into the Minkowski space and new quasi-local mass" by M.-T. Wang and S.-T. Yau

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  • $\begingroup$ Wow, this is fantastic! I really appreciate it! Thank you so much :) $\endgroup$ – MKF Jul 14 '15 at 0:26
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Well, Willie Wong just gave a while ago a great answer for this kind of things

Open problems in General Relativity

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