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

Abstract

Although the super-energy Bel-Robinson tensor gives a desirable gravitational energy-momentum in a small sphere region, the angular-momentum is vanishing. Intuitively, it should be non-zero. Our present work shows that indeed the angular momentum is non-vanishing under the continuity equation requirement. Meanwhile this angular momentum can be converted as a ``Poynting" vector. In addition, by the analog, we also constructed the four ``Maxwell" equations in general relativity.