2014/05/30 by Lau Loi So, So, Lau Loi
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Experimental and Theoretical Physics Studies #gr-qc
paper · pdf · doi:10.48550/arxiv.1405.7883
7 pages, a major revision of arXiv:1302.2412
arxiv created 2014/05/30 · arxiv updated 2014/06/02
For describing the non-negative gravitational energy-momentum in terms of a pure Bel-Robinson type energy-momentum in a quasi-local 2-surface, both the Bel-Robinson tensor B and tensor V are suitable. We have found that this Bel-Robinson type energy-momentum can be modified such that it satisfies the Lorentz covariant, future pointing and non-spacelike properties. We find that these particular quasi-local energy-momentum properties can be obtained from (i): B or V plus a tensor S in a small sphere limit, or (ii): directly evaluating the energy-momentum of B or V in a small ellipsoid region. (iii): calculate the total energy using the Landau-Lifshitz pseudotensor in a small ellipsoid, from Jupiter's tidal force to Io in Schwarzchild spacetime, in an elliptic orbit.