Einstein-Cartan-Dirac equations in the Newman-Penrose formalism
General Relativity and Quantum Cosmology
2018-10-03 v2 High Energy Physics - Theory
Quantum Physics
Abstract
We formulate the Einstein-Cartan-Dirac equations in the Newman-Penrose (NP) formalism, thereby presenting a more accurate and explicit analysis of previous such studies. The equations show in a transparent way how the Einstein-Dirac equations are modified by the inclusion of torsion. In particular, the Hehl-Datta equation is presented in NP notation. We then describe a few solutions of the Hehl-Datta equation on Minkowski space-time, and in particular report a solitonic solution which removes the unphysical behavioiur of the corresponding Dirac solution. The present work serves as a prelude to similar studies for non-degenerate Poincare gauge gravity.
Keywords
Cite
@article{arxiv.1804.11334,
title = {Einstein-Cartan-Dirac equations in the Newman-Penrose formalism},
author = {Swanand Khanapurkar and Abhinav Varma and Nehal Mittal and Navya Gupta and Tejinder P. Singh},
journal= {arXiv preprint arXiv:1804.11334},
year = {2018}
}
Comments
32 pages, 4 figures, Section 5.4 on plane waves rewritten