The mean gauges in bimetric relativity

Torsello, Francesco

doi:10.1088/1361-6382/ab4ccf

Cited by 13 publications

(27 citation statements)

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“…10 Hence, we can choose the Levi-Civita connection of the conformal spatial metric χ to define the covariant conformal connection in (3.14). The consequences of this choice are described in more detail in [59].…”

Section: The Covariant Extension Of the Bssn Formulationmentioning

confidence: 99%

Covariant BSSN formulation in bimetric relativity

Torsello

Kocic

Högås

et al. 2019

Class. Quantum Grav.

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Numerical integration of the field equations in bimetric relativity is necessary to obtain solutions describing realistic systems. Thus, it is crucial to recast the equations as a well-posed problem. In general relativity, under certain assumptions, the covariant BSSN formulation is a strongly hyperbolic formulation of the Einstein equations, hence its Cauchy problem is well-posed. In this paper, we establish the covariant BSSN formulation of the bimetric field equations. It shares many features with the corresponding formulation in general relativity, but there are a few fundamental differences between them. Some of these differences depend on the gauge choice and alter the hyperbolic structure of the system of partial differential equations compared to general relativity. Accordingly, the strong hyperbolicity of the system cannot be claimed yet, under the same assumptions as in general relativity. In the paper, we stress the differences compared with general relativity and state the main issues that should be tackled next, to draw a road map towards numerical bimetric relativity.

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Section: The Covariant Extension Of the Bssn Formulationmentioning

confidence: 99%

Covariant BSSN formulation in bimetric relativity

Torsello

Kocic

Högås

et al. 2019

Class. Quantum Grav.

Self Cite

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“…The package was written during the work to obtain the results in [23,24]. Therefore, at the present stage, it includes the covariant BSSN equations written as abstract tensors, together with the bimetric 3 `1 and BSSN decompositions [16,23].…”

Section: Discussionmentioning

confidence: 99%

“…This is the first step towards the numerical integration of the equations and the attainment of solutions to the BFE describing sensible bimetric physical systems, e.g., nonlinear bimetric gravitational collapse. bimEX was developed with this goal in mind, and was the workhorse in obtaining the results in [23,24], and reproducing the results in [16]. The name of the package is an acronym for "bimetric exact computations".…”

Section: Motivation and General Descriptionmentioning

confidence: 99%

“…In bimetric relativity, there is the possibility to set χ as the background geometry for γ and ϕ, hence the assumption of time-independency can be relaxed. See [24] for more details. 3 Note that choosing an ansatz for p a and q i is equivalent to choosing an ansatz for β i and r β i .…”

Section: Bimetric Relativity and Its Primary Variablesmentioning

confidence: 99%

“…To reproduce the results in [16] and obtain the results in [23,24], we used the algorithm in Listing 7, since the chosen ansatz imply that δ ´1R o J δR o is diagonal, and the function MatrixPower is efficient enough. In this case, the algorithm in Listing 9 gives a much more complicated expression, which has to be simplified in a second step to give the simpler expression obtained with the algorithm in Listing 7.…”

Section: Return[s]; ]mentioning

confidence: 99%

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

2020
Computer Physics Communications
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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.

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