  A proposal for the gravitational energy-momentum tensor, known in the
literature as the square root of Bel-Robinson tensor, is analyzed in detail.
Being constructed exclusively from the Weyl part of the Riemann tensor, such
tensor encapsulates the geometric properties of free gravitational fields in
terms of optical scalars of null congruences: making use of the general
decomposition of any energymomentum tensor, we explore the thermodynamic
interpretation of such geometric quantities. While the matter energy-momentum
is identically conserved due to Einstein's field equations, the SQBR is not
necessarily conserved and dissipative terms could arise in its vacuum
continuity equation. We discuss the possible physical interpretations of such
mathematical properties.
