On the Notions of Energy Tensors in Tetrad-Affine Gravity

Abstract

We are concerned with the precise modalities by which mathematical constructions related to energy tensors can be adapted to a tetrad-affine setting. We show that, for fairly general gauge field theories formulated in that setting, two notions of energy tensor (the canonical tensor and the stress-energy tensor) exactly coincide with no need for tweaking. Moreover, we show how both notions of energy tensor can be naturally extended to include the gravitational field itself, represented by a couple constituted by the tetrad and the spinor connection. Then we examine the on-shell divergences of these tensors in relation to the issue of local energy conservation in the presence of torsion.