Conservation Laws on Riemann-Cartan, Lorentzian and Teleparallel Spacetimes
Abstract
In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and also in the particular cases of Lorentzian and teleparallel spacetimes and (b): the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this latter concept can be rigorously defined. We examine in details some misleading and even erroneous and often quoted statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel one) theories.
Keywords
Cite
@article{arxiv.math-ph/0605008,
title = {Conservation Laws on Riemann-Cartan, Lorentzian and Teleparallel Spacetimes},
author = {Waldyr A. Rodrigues and Quintino A. G. de Souza and Roldao da Rocha},
journal= {arXiv preprint arXiv:math-ph/0605008},
year = {2008}
}
Comments
Some sections have been rewritten for better inteligibility and some new material and new references have been included and others updated. Some important misprints of the previous version have been corrected. The contents of this paper appeared in two parts in Bull. Soc. Sci. Lodz. Series 57, Ser. Res. on Deformations, 52, 37-65, 66-77 (2007)