Brown-York charges with mixed boundary conditions

A bstract We compute the Hamiltonian surface charges of gravity for a family conservative boundary conditions, that include Dirichlet, Neumann, and York’s mixed conditions defined by holding fixed conformal induced metric trace extrinsic curvature. show all considered, canonical methods give same answer as covariant phase space improved Lagrangian, prescription recently developed in literature thus supported our results. The procedure also suggests new integrable charge Einstein-Hilbert different from Komar non-Killing non-tangential diffeomorphisms. study how energy depends on choice showing both quasi-local asymptotic expressions are affected. Finally, we generalize analysis to non-orthogonal corners, confirm matching between results without any change prescription, discuss subtleties associated with this case.