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Is there an example of (2+2)-dimensional flat spacetime with neutral signature (i.e. (+,+,-,-))? ...for example the metric $ds^2=(dt_1)^2+(dt_2)^2-(dx)^2-(dy)^2$, has been studied? Are there any papers in this regard in the literature (i.e. I mean where the authors consider also the flat case)

EDITED QUESTION

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