The initial boundary value problem and quasi-local Hamiltonians in general relativity

DOI10.1088/1361-6382/ac0a86zbMath1482.83002arXiv2103.15673OpenAlexW3168792721WikidataQ114096978 ScholiaQ114096978MaRDI QIDQ5162835

Zhongshan An, Michael T. Anderson

Publication date: 5 November 2021

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.15673

zbMATH Keywords

Einstein equationsinitial boundary value problemcovariant phase spacequasi-local Hamiltonians

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Boundary value problems on manifolds (58J32) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items (4)

Finite features of quantum de Sitter space ⋮ Gravitational observatories ⋮ Black hole to cosmic horizon microstates in string/M theory: timelike boundaries and internal averaging ⋮ Thermodynamic ensembles with cosmological horizons

Cites Work

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• The Ricci flow on manifolds with boundary
• Total mean curvature, scalar curvature, and a variational analog of Brown-York mass
• Quasi-local energy-momentum and angular momentum in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
• On boundary value problems for Einstein metrics
• Reduction of symplectic manifolds with symmetry
• The initial boundary value problem for Einstein's vacuum field equation
• The existence and uniqueness of solutions of Yang-Mills equations with bag boundary conditions
• Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature.
• On geometric problems related to Brown-York and Liu-Yau quasilocal mass
• Conformal immersions of prescribed mean curvature in \(\mathbb{R}^3\)
• Continuum and discrete initial-boundary value problems and Einstein's field equations
• Boundary conditions for coupled quasilinear wave equations with application to isolated systems
• Global aspects of the Cauchy problem in general relativity
• Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires
• Covariant phase space with boundaries
• On the stability of gravity with Dirichlet walls
• Local symmetries and constraints
• General definition of “conserved quantities” in general relativity and other theories of gravity
• Setting the boundary free in AdS/CFT
• The inverse function theorem of Nash and Moser
• Dirichlet and neumann boundary value problems for Yang-Mills connections
• Canonical phase space formulation of quasi-local general relativity
• Covariant phase space, constraints, gauge and the Peierls formula
• Geometric boundary data for the gravitational field
• Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
• The conformal method and the conformal thin-sandwich method are the same
• General Relativity

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