It is (more or less) known that when defining a metric one can provide a parameter
signature, e.g +1 for Riemannian metrics or -1 for Lorentzian metrics; and it is also known that one can parametrise the epsilon tensor with a metric.
I'm interested, however, in a generic epsilon tensor defined for a Lorentzian signature... without specifying a metric (because I want to consider spacetimes with diferent dimensionality). I tried the following, and it seems to work:
Is the above proposal equivalent to assigning a
signature = -1 to the epsilon?