By Andrzej Trautman (auth.), Peter G. Bergmann, Venzo De Sabbata (eds.)
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Additional resources for Cosmology and Gravitation: Spin, Torsion, Rotation, and Supergravity
Hence the tetrad (or rather T4-) people who searched for this quantity for quite a long time, were not all that wrong, as will become clear from the lecture of Nitsch. 4, for a V linear in curvature, €~i turns out to be just the Einstein tensor of the U4 , for a quadratic lagrangian €~i is of the type of a contracted Bel-Robinson tensor (see ) or, to speak in electrodynamical terms, of the type of Minkowski's energy-momentum tensor. tIn words we could summarize the structure of the field equations as follows: gauge covariant divergence of field momentum = (gauge + material) current.
The rotons should be suppressed in the limit of vanishing curvature (then the rotons' kinetic energy is zero). In other words, curvature is no longer at our disposal and the torsion-square piece has to play the role of the gravitons' kinetic energy. And we know from teleparallelism that it can do so. Since we don't need the curvature scalar any longer, we drop it and put X = 00, even if that is not necessarily implied by the arguments given. 54) has a very plausible structure both from the point of view of allowing rotons to propagate and of being consistent with macroscopic gravity in an enforced T4-limit.
34) is of the desired type, because it is a second-order field equation in ekY. 23) that JC~ij can only be linear and homogeneous in Fki Y. *Some attempts to relate torsion to weak interaction, were recently criticized by DeSabbata and Gasperini. 23). 34), would be just an einsteinian type of field equation provided the constants d l , d2, and d 3 were appropriated fixed. Our goal was to suppress the rotons. 36) the choice of a V4 would kill the whole lagrangian. e. 36) and onto our U4-spacetime the additional requirement of vanishing curvature.