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I know that in the absence of soures, i.e. matter fields the Ricci scalar is zero. This is synonymous with saying that the Ricci scalar vanishes in vacuum and that the resulting space is flat. However, this is simply a

*sufficient*requirement.

Is it also

*necessary*? That is to say, if the Ricci tensor is found to be zero in a very complicated spacetime (I work in brane worlds) does that also mean that the space is vacuum? I am pretty sure that it is flat, since geometrically R=0 implies flatness...

To me is seems that this is indeed the case, but my supervisor and another guy I know from mathematics says it might not be (he wasnt sure).

Thank you in advance,

/blake