The initial boundary value problem and quasi-local Hamiltonians in general relativity
Zhongshan An, Michael T Anderson
Abstract
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 analyze 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.
Topics & Concepts
PhysicsBoundary value problemCovariant transformationGeneral relativityHamiltonian (control theory)Mathematical physicsFour-forceDirichlet boundary conditionPhase spaceMathematics of general relativityMixed boundary conditionBoundary (topology)Classical mechanicsTheory of relativityInitial value problemSpacetimeDirichlet distributionSpace (punctuation)Numerical relativityNeumann boundary conditionHamiltonian systemHamiltonian mechanicsBoundary conformal field theoryMathematical analysisSpace timeQuantum Mechanics and Non-Hermitian PhysicsSpectral Theory in Mathematical PhysicsNonlinear Waves and Solitons