2014/08/27 by Peng Huang, Huang, Peng, Fang-Fang Yuan +1
Earth and Planetary Sciences · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geophysics and Gravity Measurements #gr-qc
paper · pdf · doi:10.48550/arxiv.1408.6412
12 pages, corrected typos, rearranged references
openalex publication_date 2014/08/27 · arxiv created 2015/04/13 · arxiv updated 2015/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For teleparallel gravity in four dimensions, Lucas and Pereira have shown that a generalized Hodge dual for torsion tensor can be defined with coefficients determined by mathematical consistency. In this paper, we demonstrate that a direct generalization to other dimensions fails and no new generalized Hodge dual operator could be given. Furthermore, if one enforces the definition of a generalized Hodge dual to be consistent with the action of teleparallel gravity in general dimensions, the basic identity for any sensible Hodge dual would require an ad hoc definition for the second Hodge dual operation which is totally unexpected. Therefore, we conclude that at least for the torsion tensor, the observation of Lucas and Pereira only applies to four dimensions.