Einstein-Cartan-Dirac equations in the Newman-Penrose formalism

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.

arXiv comment32 pages, 4 figures, Section 5.4 on plane waves rewritten

References in corpus (5)

• Conceptual Problems in Quantum Gravity and Quantum Cosmology
• On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B
• Spin-torsion coupling and gravitational moments of Dirac fermions: theory and experimental bounds
• Fermions without Vierbeins in Curved Space-Time
• A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass

Cited by in corpus (4)

• Einstein-Cartan-Dirac gravity with $U(1)$ symmetry breaking
• Cosmological bounces, cyclic universes, and effective cosmological constant in Einstein-Cartan-Dirac-Maxwell theory
• Non-relativistic limit of Einstein-Cartan-Dirac equations
• Generalized uncertainty principle for a Dirac fermion in a torsion field