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.
Highlights
The parametrized post-Newtonian (PPN) formalism [1,2,3,4,5,6,7] is an indispensable tool for testing the viability of gravity theories
In the PPN formalism it is assumed that the source of gravity is the energy-momentum tensor αβ of a perfect fluid (1), which defined by xPPN is a tensor on M4 denoted by EnergyMomentum[-T4α, -T4β]
We present a number of utility functions defined by xPPN, which can be used to manipulate terms which typically appear in the post-Newtonian expansion, perform necessary computational steps and solve the gravitational field equations in terms of the post-Newtonian potentials and parameters listed in the previous sections
Summary
The parametrized post-Newtonian (PPN) formalism [1,2,3,4,5,6,7] is an indispensable tool for testing the viability of gravity theories. It comes with numerous functions to define and manipulate tensorial expressions, and includes concepts such as induced metrics on hypersurfaces orthogonal to a vector field, or component calculations in xCoba, which can be used to achieve a 3 + 1 split of tensorial expressions The former is employed, for example, for cosmological perturbation theory in the xPand package [11], in conjunction with the xPert package [12] for general tensor perturbations. Even though it is possible to implement the PPN formalism using the existing functionality mentioned above, it appears simpler to overcome the aforementioned difficulties by using a different approach both to the 3 + 1 split and the perturbative expansion, without using the induced metric framework or the xCoba and xPert packages This is the approach followed by xPPN. We use lowercase letters for coordinate indices and uppercase letters for Lorentz indices, where in both cases Greek indices run from 0 to 3 and belong to spacetime, while Latin indices run from 1 to 3 and belong to space only
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
