Poincare gauge gravity: selected topics

TL;DR

This paper reviews the classical Poincare gauge theory of gravity, highlighting its geometric structure, analyzing quadratic models, and showing Einstein's theory as a special case, while discussing solution methods.

Contribution

It provides a comprehensive overview of the Poincare gauge gravity framework, including formalism, model analysis, and solution construction techniques.

Findings

Einstein's theory emerges as a degenerate case of quadratic Poincare models.

The Lagrange-Noether formalism is fully developed for this gravity theory.

The double duality method aids in constructing exact solutions.

Abstract

In the gauge theory of gravity based on the Poincare group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy-momentum) and the spin are treated on an equal footing as the sources of the gravitational field. The corresponding spacetime manifold carries the Riemann-Cartan geometric structure with the nontrivial curvature and torsion. We describe some aspects of the classical Poincare gauge theory of gravity. Namely, the Lagrange-Noether formalism is presented in full generality, and the family of quadratic (in the curvature and the torsion) models is analyzed in detail. We discuss the special case of the spinless matter and demonstrate that Einstein's theory arises as a degenerate model in the class of the quadratic Poincare theories. Another central point is the overview of the so-called double duality method for constructing of the exact solutions of the classical field equations.