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

Authors
• 1 University of Tartu, W. Ostwaldi 1, Tartu, 50411, Estonia , Tartu (Estonia)
Type
Published Article
Journal
The European Physical Journal C
Publisher
Springer-Verlag
Publication Date
Jun 07, 2021
Volume
81
Issue
6
Identifiers
DOI: 10.1140/epjc/s10052-021-09183-9
Source
Springer Nature
Green

## 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3+1$$\end{document} 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.

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