A weighted de Rham operator leading to local potentials for Riemann and Weyl tensors
2006 (English)In: XXVIII Spanish Relativity Meeting E.R.E. A Century of Relativity Physics,2005 / [ed] Mornas, L; Alonso, JD, Melville, NY, USA: American Institute of Physics (AIP), 2006, 291- p.Conference paper (Other academic)
By defining a weighted de Rham operator for r-fold forms we obtain an associated superpotential for all tensors (considered as r-fold forms), in all dimensions. From this superpotential we deduce, in a straightforward and natural manner, the existence of 2r potentials for all r-fold forms. By specialising this result, we are able to obtain a pair of potentials for the Riemann tensor, and a single (2,3)-form potential for the Weyl tensor. This latter potential is the n-dimensional version of the double dual of the classical four dimensional (2,1)-form Lanczos potential. We also demonstrate that the new weighted de Rham operator is the natural operator to use in the Laplace-like equation for the Riemann tensor.
Place, publisher, year, edition, pages
Melville, NY, USA: American Institute of Physics (AIP), 2006. 291- p.
, AIP Conference Proceedings, ISSN 0094-243X
IdentifiersURN: urn:nbn:se:liu:diva-30240ISI: 000239410700021Local ID: 15745ISBN: 0-7354-0333-3OAI: oai:DiVA.org:liu-30240DiVA: diva2:251062
28th Spanish Relativity Meeting Oviedo, SPAIN SEP 06-10, 2005