# Regular initial data

I have a very basic question. What exactly is meant by "regular" initial data in general relativity? Does it mean smooth? at least $C^{2}$?

All literature on the subject just uses this term without exact explanation, so it seems that it's something very trivial, but I just wanted to know for sure.

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With Bianchi identities it seems better than the metric tensor would be, at least, 3 times differentiable, but I think that the standard is infinitely differentiable, so $C^{\infty}$. –  Trimok Jun 10 '13 at 9:46
Could you include an example of where the term is being used so that we can have some context. The answer to this could very well be context-dependent after all. –  joshphysics Jun 10 '13 at 16:30
@joshphysics well,it's used literally in every book/paper. Some examples: link, on page 2 talks about "sufficiently regular" without explanation what it is, or another example link –  ConciseAndClear Jun 11 '13 at 7:32