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

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.

The mean gauges in bimetric relativity

“…We do know it in the spherically symmetric case, though, hence in this case we can compute the time derivatives of Λ s , R and χ. The equations in spherical symmetry are presented in Appendix B.5, and were computed using the Mathematica package bimEX [42].…”

“…In this appendix we reduce to spherical symmetry the most relevant equations introduced in the main text. The computations were done with the Mathematica package bimEX [42]. The spherically symmetric ansatz with the metric g and f sharing the same Killing vector fields is [26] The metrics γ and ϕ share the background geometry, which is the spatial part of the flat metric in spherical coordinates,…”

Constraints on bimetric gravity from Big Bang nucleosynthesis

“…This means that structure formation cannot be analyzed using linear perturbation theory, instead it is necessary to solve the full non-linear equations of motion [43,44,46], requiring a stable (well-posed) form of the equations of motion. Partial progress has been made in that direction [48][49][50][51][52][53][54][55], but a well-posed form of the equations of motion is still unknown. The bimetric action (Hassan-Rosen action) is,…”

Snowmass2021 Cosmic Frontier White Paper: Numerical relativity for next-generation gravitational-wave probes of fundamental physics

“…Studies focusing on the formation or evolution of single black holes were considered in Lorentzviolating theories [177,178], massive gravity [179][180][181][182][183][184], quadratic gravity [185][186][187][188][189][190][191][192][193][194], or higher curvature effective theories [195]. These have shown that black holes may develop scalar hair during their collapse, e.g., if described in quadratic and higher derivative gravity.…”