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sheaf
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Back in the 1980s, a lot of work (Hawking et al) was done on deriving semiclassical and quantum gravity results on spacetimes with Euclidean signature. The connection with the Lorentzian signature versions was then made by analytic continuation. Does anyone know - are there any generic conditions which can be stated which ensure that a Lorentzian signature metric can be analytically continued into the complex domain and there posess a Euclidean signature section ? Or alternatively, what are the obstructions to analytic continuation into the Euclidean domain ?