What is the "ontology" of general relativity ? Hi, First of all, though I know some GR, I'm far from an expert on it. I used to think of the "ontology" of GR as being a 4-dimensional manifold with a metric connection on it, but apparently that doesn't fly, because of the "hole argument": http://plato.stanford.edu/entries/spacetime-holearg/ I used to think that general covariance simply meant that we could choose arbitrary coordinates on this manifold, but it seems that this is not sufficient. So my question is: if the "ontology" of GR is NOT a 4-dim. manifold + metric connection, then what is this ontology ? What, according to (classical) GR, is "out there" ; how do relativists see their subject ? Or can we still see the ontology of GR as being a 4-dim manifold + metric connection, and the different physical descriptions as "gauge-equivalent" ?