# Parametrized Post-Newtonian Expansion of Chern-Simons Gravity

## TL;DR

This paper analyzes the post-Newtonian expansion of Chern-Simons gravity, revealing that its parameters match general relativity except for a new term linked to the Chern-Simons coupling, which could be tested experimentally.

## Contribution

It provides the first detailed mapping of Chern-Simons gravity to the PPN formalism, identifying a unique correction term and exploring its physical implications.

## Key findings

- Chern-Simons PPN parameters match those of GR.
- A new correction term proportional to the Chern-Simons coupling is identified.
- Potential for experimental bounds on Chern-Simons parameters.

## Abstract

We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in Chern-Simons gravity with a perfect fluid source. In particular, we study the mapping of this solution to the parameterized post-Newtonian formalism to 1 PN order in the metric. We find that the PPN parameters of Chern-Simons gravity are identical to those of general relativity, with the exception of the inclusion of a new term that is proportional to the Chern-Simons coupling parameter and the curl of the PPN vector potentials. We also find that the new term is naturally enhanced by the non-linearity of spacetime and we provide a physical interpretation for it. By mapping this correction to the gravito-electro-magnetic framework, we study the corrections that this new term introduces to the acceleration of point particles and the frame-dragging effect in gyroscopic precession. We find that the Chern-Simons correction to these classical predictions could be used by current and future experiments to place bounds on intrinsic parameters of Chern-Simons gravity and, thus, string theory.