The geometrical meaning of time-some cosmological implications

It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type gμv diag(1, -1, -1, -1) this is usually presented as an independent axiom of the theory, which cannot be deduced from other assumptions. The meaning of this assertion is that a specific coordinate (the temporal coordinate) is given a unique significance with respect to the other spatial coordinates. It was shown that the above assertion is a consequence of requirement that the metric of empty space should be linearly stable and need not be assumed. Some cosmological implications of the above result will be suggested.