The Stability of Lorentzian Space-Time
  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. 
Asher Yahalom