General Properties of Bel Currents

The divergence-free property of the Bel tensor in some cases allows us to obtain conserved currents in the same way as it is usually done using the energy-momentum tensor, once there are Killing vector fields defined in our spacetime. But the divergence of the Bel tensor does not vanish in general and the Bel currents, if not conserved, can lead to the description of the interchange of some quantities between the gravitational and other physical fields which are indeed conserved as a whole, as it has been recently shown for the coupling with a scalar field. Nevertheless, the Bel currents are shown to be conserved automatically depending on some geometrical properties of the Killing vectors used in their construction, independently of the matter content. These properties are the analogous to some very well known statements concerning the energy-momentum tensor.