Speaker
Description
In this work, we compute the Hamiltonian surface charges of gravitational systems under a range of conservative boundary conditions, including Dirichlet, Neumann, and York’s mixed boundary conditions, where the conformal induced metric and the trace of the extrinsic curvature are fixed. We demonstrate that for all these boundary conditions, the canonical approach produces results consistent with those obtained from covariant phase space methods enhanced by an added boundary Lagrangian—a recently proposed technique in the literature, which our findings support. This study further explores the impact of boundary conditions on energy, showing that both quasi-local and asymptotic energy expressions are sensitive to the choice of boundary condition. Additionally, our approach suggests a novel integrable charge for the Einstein-Hilbert Lagrangian that deviates from the Komar charge when considering non-Killing and non-tangential diffeomorphisms, offering a potential alternative in such contexts.
