Gravitational energy for GR and Poincaré gauge theories: A covariant Hamiltonian approach

Chiang Mei Chen, James M. Nester, Roh Suan Tung

研究成果: 書貢獻/報告類型篇章同行評審

1 引文 斯高帕斯(Scopus)


Our topic concerns a long standing puzzle: The energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy- momentum and angular momentum/center-of-mass momentum (CoMM). It is known that these quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. In the first part of this work, we review some early history, much of it not so well known, on the subject of gravitational energy in Einstein's general relativity (GR), noting especially Noether's contribution. In the second part, we review (including some new results) much of our covariant Hamiltonian formalism and apply it to Poincaré gauge theories of gravity (PG), with GR as a special case. The key point is that the Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and furthermore, it determines the boundary conditions for the dynamical variables. Energy-momentum and angular momentum/CoMM are associated with the geometric symmetries under Poincaré transformations. They are best described in a local Poincaré gauge theory. The type of spacetime that naturally has this symmetry is Riemann-Cartan spacetime, with a metric compatible connection having, in general, both curvature and torsion. Thus our expression for the energy-momentum of physical systems is obtained via our covariant Hamiltonian formulation applied to the PG.

主出版物標題One Hundred Years of General Relativity
主出版物子標題From Genesis and Empirical Foundations to Gravitational Waves, Cosmology And Quantum Gravity
發行者World Scientific Publishing Co. Pte Ltd
出版狀態已出版 - 26 5月 2017


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