  It is stated in many text books that the any metric appearing in general
relativity should be locally Lorentzian i.e. of the type $\eta_\mn = {\rm diag}
(1,-1,-1,-1)$ 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 stability analysis of the
Einstein \eqs and need not be assumed.
