On quasi-local Hamiltonians in General Relativity

Abstract

We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consistent definition of quasi-local energy in GR requires, at a minimum, a framework based on the (currently unknown) geometric well-posedness of the initial boundary value problem for the Einstein equations.

9 pages

References in corpus (4)

• Quasilocal mass in general relativity
• Boundary conditions for coupled quasilinear wave equations with application to isolated systems
• Initial boundary value problems for Einstein's field equations and geometric uniqueness
• Absorbing boundary conditions for Einstein's field equations