An unique alternative non-negative gravitational energy tensor to the Bel-Robinson tensor in the quasilocal small sphere limit

2010/06/28 by Lau Loi So, So, Lau Loi
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Galaxies: Formation, Evolution, Phenomena #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #gr-qc

paper · pdf · doi:10.48550/arxiv.1006.5272

13 pages, a major revision of arXiv:0901.4828

arxiv created 2010/06/28 · openalex publication_date 2010/06/28 · arxiv updated 2010/06/29 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The Bel-Robinson tensor B_αβμν gives a positive definite gravitational energy in the quasilocal small sphere limit approximation. However, there is an alternative tensor V_αβμν that was proposed recently that offers the same positivity as B_αβμν does. We have found that V_αβμν is the unique alternative tensor with B_αβμν which implies that these two tensors are a basis for expressions that have the desirable non-negative gravitational energy in the small sphere limit. In other words, the `energy-momentum' density according to B_αβμν and V_αβμν are on equal footing at the same limit.

Citations

• An alternative non-negative gravitational energy tensor to the Bel-Robinson tensor

Related

• An alternative non-negative gravitational energy tensor to the Bel-Robinson tensor
• The modification of the Bel-Robinson energy-momentum
• Gravitational energy in small regions for the quasilocal expressions in orthonormal frames
• Dominant property for the Bel-Robinson tensor and tensor S
• Modification of the Bel-Robinson type energy-momentum