English

Gravitational energy is well defined

General Relativity and Quantum Cosmology 2018-11-15 v1 High Energy Physics - Theory

Abstract

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 \emph{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 non-dynamical 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 non-negative Wang-Yau mass.

Keywords

Cite

@article{arxiv.1805.07692,
  title  = {Gravitational energy is well defined},
  author = {Chiang-Mei Chen and Jian-Liang Liu and James M. Nester},
  journal= {arXiv preprint arXiv:1805.07692},
  year   = {2018}
}

Comments

7 pages, Honorable Mention in the 2018 Essay Competition of the Gravity Research Foundation

R2 v1 2026-06-23T02:01:40.779Z