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Describing the gravitational energy-momentum, the super-energy Bel-Robinsontensor is the best candidate. In the past, people seems only explore the lowestorder: the electric part $E_{ab}$ and magnetic part $B_{ab}$ for the Riemanntensor. These two components are related with the static case, however, for theenergy transfer situation, one may need to consider the time varying$\dot{E}_{ab}$ and $\dot{B}_{ab}$. Here we use $(\dot{E}_{ab},\dot{B}_{ab}$) tostudy the energy-momentum for the Bel-Robinson tensor in a small sphere limit.Meanwhile, our result illustrates how the gravitational field carries the4-momentum including this extra information.

The gravitational energy-momentum for the super-energy Bel-Robinson tensor