# $\mathtt{bimEX}$: A Mathematica package for exact computations in $3+1$ bimetric relativity

## TL;DR

bimEX is a Mathematica package designed for exact symbolic and component-based computations in 3+1 bimetric relativity, facilitating the derivation of complex equations in this field.

## Contribution

It introduces a new Mathematica package that streamlines handling multiple metrics and deriving bimetric equations in specific charts, enhancing computational efficiency and accuracy.

## Key findings

- Successfully derived covariant BSSN bimetric equations
- Reproduced 3+1 equations in spherical polar coordinates
- Validated package performance in spherical symmetry scenarios

## Abstract

We present $\mathtt{bimEX}$, a Mathematica package for exact computations in 3$+$1 bimetric relativity. It is based on the $\mathtt{xAct}$ 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 $\mathtt{xAct}$. 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.