Evaluation of the ADM mass and center of mass via the Ricci tensor

DOI10.1090/proc12726zbMath1335.83012arXiv1408.3893OpenAlexW2963995404MaRDI QIDQ2789872

Luen-Fai Tam, Pengzi Miao

Publication date: 2 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.3893

zbMATH Keywords

Ricci tensorHamiltonian formulationdensity theoremasymptotically flat manifoldADM masscenter of mass

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Gravitational energy and conservation laws; groups of motions (83C40) Global Riemannian geometry, including pinching (53C20) Approximation procedures, weak fields in general relativity and gravitational theory (83C25)

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Cites Work

• A note on center of mass
• Localizing solutions of the Einstein constraint equations
• Role of surface integrals in the Hamiltonian formulation of general relativity
• The Poincaré group as the symmetry group of canonical general relativity
• Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature
• The energy and the linear momentum of space-times in general relativity
• On the asymptotics for the vacuum Einstein constraint equations
• On the center of mass in general relativity
• Coordinate Invariance and Energy Expressions in General Relativity
• The mass of an asymptotically flat manifold
• The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation
• Foliation by Constant Mean Curvature Spheres on Asymptotically Flat Manifolds
• Scalar Curvature and the Einstein Constraint Equations
• On the center of mass of isolated systems with general asymptotics
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