The gravitational origin of the distinction between space and time

To the ordinary human it is obvious that there is a clear distinction between the spatial dimensions, in which one can go either way, and the temporal dimension, in which one seems only to move forward. But the uniqueness of time is also rooted in the standard presentation of general relativity, in which the metric of spacetime is locally Lorentzian, i.e. η_μν = diag(1, -1, -1, -1). This is presented as an independent axiom of the theory, which cannot be deduced. In this essay I will claim otherwise. I will show that the existence of time should not be enforced on the gravitational theory of general relativity but rather should be deduced from it. The method of choice is linear stability analysis of flat spacetimes.