Dominant property for the Bel-Robinson tensor and tensor S

2016/12/22 by Lau Loi So, So, Lau Loi
Engineering · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Elasticity and Material Modeling #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc

paper · pdf · doi:10.48550/arxiv.1612.07664

4 pages

arxiv created 2016/12/22 · openalex publication_date 2016/12/22 · arxiv updated 2016/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Bel-Robinson tensor contains many nice mathematical properties and its dominant energy condition is desirable for describing the positive gravitational energy. The dominant property is a basic requirement for the quasi-local mass, i.e., in small sphere limit. We claim that there exists another option, a linear combination between the Bel-Robinson tensor B and tensor S, which contributes the same dominant property. Moreover, using the 5 Petrov types as the verification, we found that this dominant property justification for the Bel-Robinson tensor can be simplified as examining B₀₀₀₀≥|B_αβ00| and B₀₀₀₀≥|B₀₁₂₃|, instead of B₀₀₀₀≥|B_αβλσ| for all α,β,λ,σ=0,1,2,3.

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