We take as our basic principle that the Lagrangian and the Hamiltonian formulations of general relativity should be equivalent. It is then possible to choose the gauge transformations so as to be projectable under the Legendre map from configuration-velocity space (the tangent bundle) to phase space (the cotangent bundle). This projectability requirement then implies that gauge transformations in general relativity (we study in particular spacetimes with a Yang-Mills field) must depend in a specific way on the lapse and shift of the metric. This talk outlines the arguments and presents some of the results of the application of these principles.
SHEPLEY, L. C.; PONS, J. M.; and SALISBURY, D. C. (2000) "Gauge Transformations in General Relativity - A Report," Turkish Journal of Physics: Vol. 24: No. 3, Article 24. Available at: https://journals.tubitak.gov.tr/physics/vol24/iss3/24