The initial boundary value problem and quasi-local Hamiltonians in General Relativity

Abstract

We discuss relations between the initial boundary value problem (IBVP) and quasi-local Hamiltonians in GR. The latter have traditionally been based on Dirichlet boundary conditions, which however are shown here to be ill-posed for the IBVP. We present and analyse several other choices of boundary conditions which are better behaved with respect to the IBVP and carry out a corresponding Hamiltonian analysis, using the framework of the covariant phase space method.

arXiv comment22 pages

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• Freelance Holography, Part I: Setting Boundary Conditions Free in Gauge/Gravity Correspondence
• The Cosmological Switchback Effect II
• Freelance Holography, Part II: Moving Boundary in Gauge/Gravity Correspondence
• Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter