Nother charges, Brown-York quasilocal energy, and related topics

The Lagrangian proposed by York and the covariant first-order Lagrangian fo r general relativity are reviewed. They both deal with the (vacuum) gravita tional field on a reference background and were conjectured to be equivalen t. The two corresponding actions are compared and we show that the first on e can in fact be obtained from the latter under suitable hypotheses. A cond itioned correspondence among Nother conserved quantities of covariant first -order Lagrangian, Brown-York quasilocal energy and the standard ADM Hamilt onian is also established. (C) 2001 American Institute of Physics.