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

In the 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 Tk μ and the “spin” angular momentum density Skl μ of the gravitational field. They are both space-time vector densities, and transform as tensors under global SL(2, C)transformations. Under local internal translation, Tk μ is invariant, while Skl μ transforms inhomogeneously. The dynamical energy-momentum density Tk μ and the “spin” angular momentum density Skl μ 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 Poincaré gauge transformations. The corresponding discussions in extended new general relativity which is obtained as a teleparallel limit of 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 total (=spin+orbital) angular momentum for asymptotically flat space-time. The tensorial properties of canonical energy-momentum and “extended orbital angular momentum” densities are also examined. 04.50.+h Typeset using REVTEX Electronic address : [email protected]