𝚋𝚒𝚖𝙴𝚇: A Mathematica package for exact computations in 3+1 bimetric relativity

04/23/2019

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by   Francesco Torsello, et al.

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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.