xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica

TL;DR

The paper introduces xPPN, a Mathematica package built on xAct, that automates the PPN formalism's tensor decomposition and perturbative expansion for various gravity theories.

Contribution

It provides the first comprehensive implementation of the PPN formalism in Mathematica, supporting multiple geometric frameworks and simplifying calculations in gravity research.

Findings

Automates 3+1 tensor decomposition and velocity order expansion.

Supports Riemannian, teleparallel, and symmetric teleparallel geometries.

Facilitates solving field equations in metric theories of gravity.

Abstract

We present a package for the computer algebra system Mathematica, which implements the parametrized post-Newtonian (PPN) formalism. This package, named xPPN, is built upon the widely used tensor algebra package suite xAct, and in particular the package xTensor therein. The main feature of xPPN is to provide functions to perform a proper $3+1$ decomposition of tensors, as well as a perturbative expansion in so-called velocity orders, which are central tasks in the PPN formalism. Further, xPPN implements various rules for quantities appearing in the PPN formalism, which aid in perturbatively solving the field equations of any metric theory of gravity. Besides Riemannian geometry, also teleparallel and symmetric teleparallel geometry are implemented.