Energy-momentum and angular momentum densities in gauge theories of gravity

Abstract

In the $\bar{\mbox{\rm Poincaré}}$ gauge theory of gravity, which has been formulated on the basis of a principal fiber bundle over the space-time manifold having the covering group of the proper orthochronous Poincaré group as the structure group, we examine the tensorial properties of the dynamical energy-momentum density ${}^G{\mathbf{T}}_k{}^{\mu }$ and the ` ` spin" angular momentum density ${}^G{\mathbf{S}}_{kl}{}^{\mu }$ of the gravitational field. They are both space-time vector densities, and transform as tensors under {\em global} $SL(2,C)$- transformations. Under {\em local} internal translation, ${}^G{\mathbf{T}}_k{}^{\mu }$ is invariant, while ${}^G{\mathbf{S}}_{kl}{}^{\mu }$ transforms inhomogeneously. The dynamical energy-momentum density ${}^M{\mathbf{T}}_k{}^{\mu }$ and the ` ` spin" angular momentum density ${}^M{\mathbf{S}}_{kl}{}^{\mu }$ of the matter field are also examined, and they are known to be space-time vector densities and to obey tensorial transformation rules under internal $\bar{\mbox{\rm Poincaré}}$ gauge transformations. The corresponding discussions in extended new general relativity which is obtained as a teleparallel limit of $\bar{\mbox{\rm Poincaré}}$ gauge theory are also given, and energy-momentum and ` ` spin" angular momentum densities are known to be well behaved. Namely, they are all space-time vector densities, etc. In both theories, integrations of these densities on a space-like surface give the total energy-momentum and {\em total} (={\em spin}+{\em orbital}) angular momentum for asymptotically flat space-time. The tensorial properties of canonical energy-momentum and ` ` extended orbital angular momentum" densities are also examined.

18 pages

References in corpus (1)

• Gravitational Energy-Momentum Density in Teleparallel Gravity

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