It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type ημv = diag (1,−1,−1,−1) this is usually presented as an independent axiom of the theory, which can not be deduced from other assumptions. In this work we show that the above assertion is a consequence of a standard linear stability analysis of the Einstein equations and need not be assumed.
