Energy-Momentum and Angular Momentum Densities in Poincaré Gauge Theory of Gravity

Abstract

In Poincaré gauge theory of gravity, we examine energy-momentum and angular momentum densities of source of the gravitational field (gauge potentials Akμ, Aklμ). There are two types of these quantities, the Hilbert-type densities $\mbox{$\Theta $}_{k}{}^{\mu },\, \mbox{$\Phi $}_{kl}{}^{\mu }$ which appear in the right-hand sides of gravitational field equations, and $\, ^{M}\mbox{$T$}_{k}{}^{\mu }, \, ^{M}\mbox{$S$}_{kl}{}^{\mu }$ which are the densities (Noether currents) of the generators of $T^{4}\underline{\otimes }SL(2,C)$ transformations. We show that these are identical with each others, respectively, i.e. $\mbox{$\Theta $}_{k}{}^{\mu }\equiv \, ^{M}\mbox{$T$}_{k}{}^{\mu } ,\, \mbox{$\Phi $}_{kl}{}^{\mu }\equiv \, ^{M}\mbox{$S$}_{kl}{}^{\mu }$, which are parallel to the cases of the electromagnetic and Yang-Mills fields.