TY - JOUR

T1 - Gravitational energy for GR and Poincaré gauge theories

T2 - A covariant Hamiltonian approach

AU - Chen, Chiang Mei

AU - Nester, James M.

AU - Tung, Roh Suan

N1 - Publisher Copyright:
© 2015 World Scientific Publishing Company.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - Hamiltonian boundary term

KW - Quasi-local energy

UR - http://www.scopus.com/inward/record.url?scp=84938844517&partnerID=8YFLogxK

U2 - 10.1142/S0218271815300268

DO - 10.1142/S0218271815300268

M3 - 回顧評介論文

AN - SCOPUS:84938844517

SN - 0218-2718

VL - 24

JO - International Journal of Modern Physics D

JF - International Journal of Modern Physics D

IS - 11

M1 - 1530026

ER -