Quasi-local energy from a Minkowski reference

• Published in: General relativity and gravitation Vol. 50; no. 12; pp. 1 - 14
• Main Authors: Chen, Chiang-Mei, Liu, Jian-Liang, Nester, James M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2018; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Differential Geometry; Editor’s Choice (Research Article); Energy value; Formulations; Gravity; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Quasi-local energy; Hamiltonian; Minkowski reference
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-018-2484-z

The specification of energy for gravitating systems has been an unsettled issue since Einstein proposed his pseudotensor. It is now understood that energy-momentum is quasi-local (associated with a closed 2-surface). Here we consider quasi-local proposals (including pseudotensors) in the Lagrangian–Noether–Hamiltonian formulations. There are two ambiguities: (1) there are many possible expressions, (2) they depend on some non-dynamical structure, e.g., a reference frame. The Hamiltonian approach gives a handle on both problems. The Hamiltonian perspective helped us to make a remarkable discovery: with an isometric Minkowski reference a large class of expressions—namely all those that agree with the Einstein pseudotensor’s Freud superpotential to linear order—give a common quasi-local energy value. Moreover, with a best-matched reference on the boundary this is the Wang–Yau mass value.