Gravitational energy is well defined

Chiang Mei Chen, Jian Liang Liu, James M. Nester

Research output: Contribution to journalReview articlepeer-review

9 Scopus citations


The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy-momentum is now regarded as quasi-local (associated with a closed 2-surface). We consider the pseudotensor and quasi-local proposals in the Lagrangian-Noether-Hamiltonian formulations. There are two ambiguities: (i) many expressions, (ii) each depends on some nondynamical structure, e.g. a reference frame. The Hamiltonian approach gives a handle on both problems. Our remarkable discovery is that with a 4D isometric Minkowski reference, a large class of expressions - those that agree with the Einstein pseudotensor's Freud superpotential to linear order - give a common quasi-local energy value. With a best-matched reference on the boundary, this value is the nonnegative Wang-Yau mass.

Original languageEnglish
Article number1847017
JournalInternational Journal of Modern Physics D
Issue number14
StatePublished - 1 Oct 2018


  • Gravitational energy
  • Lagrangian-Noether-Hamiltonian formulation
  • quasi-local


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