Spinor coupling to the weak Poincare gauge theory of gravity in three dimensions

TL;DR

This paper explores how Dirac fields interact with a three-dimensional Poincare gauge gravity theory with torsion, deriving exact solutions including rotating and BTZ-like geometries, and analyzing the role of spinor condensates.

Contribution

It introduces the coupling of Dirac fields to non-propagating torsion in 3D gravity and provides explicit exact solutions, expanding understanding of fermion-gravity interactions in lower dimensions.

Findings

Derived algebraic expression for torsion in terms of spinor condensate.

Obtained circularly symmetric rotating solutions collapsing to AdS_3.

Presented a BTZ-like solution in the context of spinor-torsion coupling.

Abstract

Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of a quadratic spinor condensate plus coupling coefficients. Firstly we give circularly symmetric rotating exact solutions that collapse to $AdS_3$ geometry in the absence of the Dirac condensate. Secondly we investigate a BTZ-like solution.