Second order formalism in Poincare gauge theory

TL;DR

This paper develops a second order formalism for Poincare gauge theory, resulting in models with no higher derivatives, a GR limit, and propagating torsion, with applications to neutron stars and potential experimental detection.

Contribution

It introduces a second order formalism in Poincare gauge theory that avoids higher derivatives and allows for propagating torsion fields, connecting to Einstein-Proca systems.

Findings

Constructed models with no second or higher order derivatives.

Reduced field equations to Einstein-Proca system.

Presented approximate solutions for neutron star torsion fields.

Abstract

Changing the set of independent variables of Poincare gauge theory and considering, in a manner similar to the second order formalism of general relativity, the Riemannian part of the Lorentz connection as function of the tetrad field, we construct theories that do not contain second or higher order derivatives in the field variables, possess a full general relativity limit in the absence of spinning matter fields, and allow for propagating torsion fields in the general case. A concrete model is discussed and the field equations are reduced by means of a Yasskin type ansatz to a conventional Einstein-Proca system. Approximate solutions describing the exterior of a spin polarized neutron star are prsented and the possibility of an experimental detection of the torsion fields is briefly discussed.