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

TL;DR

This paper examines the relationship between the initial boundary value problem and quasi-local Hamiltonians in General Relativity, highlighting issues with Dirichlet boundary conditions and proposing alternative boundary conditions with a Hamiltonian analysis.

Contribution

It introduces and analyzes new boundary conditions in GR that are better suited for the IBVP, advancing the understanding of quasi-local Hamiltonians.

Findings

Dirichlet boundary conditions are ill-posed for the IBVP in GR

Alternative boundary conditions improve well-posedness

Hamiltonian analysis using covariant phase space is developed

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.