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For questions about mathematical problems arising from general relativity, the branch of physics which provides and studies the currently accepted geometric description of gravity.
3
votes
What results are immediately generalised to higher dimensions, in light of Schoen and Yau's ...
The compactness of solutions to the Yamabe problem (and its version with boundary) holds upto dimension 24 if the PMT is true. (For higher dimensions there are counterexamples.)
5
votes
2
answers
562
views
Singularity theorems for semiclassical gravity
The semi-classical Einstein equations (without a cosmological constant) are $G^{\mu \nu} = 8\pi \langle T^{\mu \nu} \rangle$.
I am told that there are serious objections as to why these equations can …