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

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.

35 pages, no figures, journal version

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• Supercomputers against strong coupling in gravity with curvature and torsion
• Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity
• The momentum constraint equation in Parameterised Post-Newtonian Cosmology
• Exploring Scalarized Einstein-Gauss-Bonnet Theories Through the Lens of Parametrized Post-Newtonian Formalism
• Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints