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

Abstract

Describing the gravitational energy-momentum, the super-energy Bel-Robinson tensor is the best candidate. In the past, people seems only explore the lowest order: the electric part $E_{ab}$ and magnetic part $B_{ab}$ for the Riemann tensor. These two components are related with the static case, however, for the energy transfer situation, one may need to consider the time varying ${\dot{E}}_{ab}$ and ${\dot{B}}_{ab}$. Here we use $({\dot{E}}_{ab},{\dot{B}}_{ab}$) to study the energy-momentum for the Bel-Robinson tensor in a small sphere limit. Meanwhile, our result illustrates how the gravitational field carries the 4-momentum including this extra information.

4 pages