why torsion free metric compatible connection ??? Why in conventional GR we choose a torsion free, metric compatible connection? Can that be derived from somewhere like physical principles/postulates or it's just a the simplest convenient choice (many terms drop from equations) that produces theory in agreement with experiment? Had we chosen a connection with torsion that is not metric compatible, would that violate any experiment? Also comment if you can on the Palatini's 'derivation' of the metric compatible torsion free connection by varying the connection in the action as a free field. Is that a real proof that the connection must be of this type or it's just an 'interesting fact' you can derive it that way?