How to detect an anti-spacetime
  Is it possible, in principle, to measure the sign of the Lapse? We show that fermion dynamics distinguishes spacetimes having the same metric but different tetrads, for instance a Lapse with opposite sign. This sign might be a physical quantity not captured by the metric. We discuss its possible role in quantum gravity. 
Marios Christodoulou, Aldo Riello, Carlo Rovelli
gr-qc hep-th