4-Dimensional Einstein Theory Extended by a 3-Dimensional Chern-Simons Term

TL;DR

This paper investigates a 4D Einstein gravity extension with a 3D Chern-Simons term, showing that apparent symmetry violations are resolved by equations of motion, with physical predictions requiring Pontryagin density to vanish.

Contribution

It demonstrates that the extended theory maintains diffeomorphism invariance through its equations of motion, clarifying the role of the Chern-Simons term in 4D gravity.

Findings

Diffeomorphism invariance is preserved by the equations of motion.

Physical predictions show little evidence of symmetry breaking.

The Pontryagin density must vanish for the theory to be consistent.

Abstract

When 4-dimensional general relativity is extended by a 3-dimensional gravitational Chern-Simons term an apparent violation of diffeormorphism invariance is extinguished by the dynamical equations of motion for the modified theory. The physical predictions of this recently proposed model show little evidence of symmetry breaking, but require the vanishing of the Pontryagin density.