Dimensionally dependent tensor identities by double antisymmetrization

DOI10.1063/1.1425428zbMath1052.53022arXivgr-qc/0105066OpenAlexW2160156031MaRDI QIDQ4830700

A. Höglund, S. Brian Edgar

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/gr-qc/0105066

Mathematics Subject Classification ID

General relativity (83C99) Applications of local differential geometry to the sciences (53B50) Local Riemannian geometry (53B20)

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Cites Work

• Some properties of the Bel and Bel-Robinson tensors
• A new gravitational energy tensor
• A new spinor identity and the vanishing of certain Riemann tensor invariants
• A complete set of Riemann invariants
• Radiation states and the problem of energy in general relativity
• Four-dimensional tensor identities of low order for the Weyl and Ricci tensors
• THE WAVE EQUATIONS FOR THE LANCZOS TENSOR/SPINOR, AND A NEW TENSOR IDENTITY
• Geometry of Gravitation and Electromagnetism
• The Splitting of the Riemann Tensor
• On the Bel - Robinson tensor
• The Lanczos potential for the Weyl curvature tensor: existence, wave equation and algorithms
• Super-energy tensors
• Normal forms for tensor polynomials. I. The Riemann tensor
• The identities of the algebraic invariants of the four-dimensional Riemann tensor. II
• Linear independence of renormalization counterterms in curved space-times of arbitrary dimensionality
• Identities of the scalars of the four-dimensional Riemannian manifold
• The identities of the algebraic invariants of the four-dimensional Riemann tensor
• The Lanczos potential for Weyl-candidate tensors exists only in four dimensions