Diffeomorphism Symmetry in the Lagrangian Formulation of Gravity

Starting from a knowledge of certain identities in the Lagrangian description, the diffeomorphism transformations of metric and connection are obtained for both the second order (metric) and the first order (Palatini) formulations of gravity. These transformations are found to be identical to the diffeomorphism transformations of the fields which establish a one-to-one mapping between the gauge and diffeomorphism symmetry.