Considering a metric $ds^2=dt^2-(1/t)dx^2$ on $R^2$.
Why is this metric _not defined_ at $t=0$ instead of just being non-smooth (non-continuous) and non-degenerate at $t=0$?
Or in other words, what is the difference (regarding metrics) between _not defined_ in a point and _not continuous_ in a point? I assumed a diverging metric coefficient means that the metric is considered not continuous (in that point).
Why is this metric _not defined_ at $t=0$ instead of just being non-smooth (non-continuous) and non-degenerate at $t=0$?
Or in other words, what is the difference (regarding metrics) between _not defined_ in a point and _not continuous_ in a point? I assumed a diverging metric coefficient means that the metric is considered not continuous (in that point).