Generalized Hodge dual for torsion in teleparallel gravity

Understand

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 \textit{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.