Formula omitted]: A Mathematica package for exact computations in [formula omitted] bimetric relativity

Abstract

We present bimEX, a Mathematica package for exact computations in 3+1 bimetric relativity. It is based on the xAct bundle, which can handle computations involving both abstract tensors and their components. In this communication, we refer to the latter case as concrete computations. The package consists of two main parts. The first part involves the abstract tensors, and focuses on how to deal with multiple metrics in xAct. The second part takes an ansatz for the primary variables in a chart as the input, and returns the covariant BSSN bimetric equations in components in that chart. Several functions are implemented to make this process as fast and user-friendly as possible. The package has been used and tested extensively in spherical symmetry and was the workhorse in obtaining the bimetric covariant BSSN equations and reproducing the bimetric 3+1 equations in the spherical polar chart. Program summaryProgram Title:bimEXProgram Files doi:http://dx.doi.org/10.17632/2s5d7csc9w.1Licensing provisions: GNU General Public License 3.0Programming language:MathematicaSupplementary material:•[1.] README file, containing instructions about how to use the working example.•[2.] Working example, constituted by the notebooks:•[(a)] bimEX_Working_Example.nb•[(b)] bimEX_Decomposition_Lists_Loader.nb•[(c)] bimEX_Decomposition_xAct_Loader.nbNature of problem: Writing the bimetric covariant BSSN equations in any desired ansatz and chart.Solution method: Definition of functions within the Mathematica package xAct, which computes all the components of the defined abstract tensors and reduce the abstract tensors to their representation in components.Additional comments: GitHub repository at https://github.com/nubirel/bimEX