Suppose we view the Einstein Field Equations (EFE) in the context of a boundary value problem with a given stress-energy tensor and boundary conditions. The problem is solved by finding a pseudo-metric.
Is there an unspoken condition that the metric to be found is locally Minkowski or is this implied by the EFE?
Specifically, do you get a different resulting pseudo-metric if you choose a different signature such as (+---) rather than (-+++)?
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