The Weiss variation in gravitation theory

Abstract: The Weiss variation formalism in mechanics and classical field theory concerns action variations that include explicit endpoint/boundary displacements. The Weiss variation is useful in field theory because it can be used to obtain expressions for the conjugate momenta and Hamiltonian without performing an explicit 3+1 decomposition beforehand. In this talk, I review the Weiss variation in mechanics, classical field theory, and in gravitation. In general relativity, one can recover (by way of an auxiliary connection formalism) a tensorial generalization of the Einstein canonical energy-momentum pseudotensor, as well as a reference-dependent Hamiltonian. After discussing the Weiss variation in general relativity, I discuss some applications of the Weiss variation formalism for modified gravity theories.