I'm a bit confused about the idea of "Change of Signature in Classical Relativity". As I see it, a metric is just a scalar function that I make up. For example, in the x,y plane I can define the functions x^2+y^2 and x^2-y^2 simultaneously. What, then, is the significance of "changing" the signature of spacetime? Why would there be one metric in one location and another metric elsewhere? I can define whatever metric I want, anywhere.