2nd-order-close-limit-approximation
https://github.com/tvdsteen/2nd-order-close-limit-approximation
Science Score: 44.0%
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Low similarity (6.9%) to scientific vocabulary
Repository
Basic Info
- Host: GitHub
- Owner: tvdsteen
- Language: Mathematica
- Default Branch: main
- Size: 1.62 MB
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- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
This ripository contains the Mathematica notebooks used to perform the calculations for my master thesis "The second order Close Limit Approximation". Three notebooks are included. The file HeadOnCollissionFinal.nb contains the calculations involved in extracting the perturbations for a head-on collission in the framework of the 2nd order close limit approximation, using a Schwarzschild background. The file M2xS2-SplitFinal.nb contains the calculations of the tensorial expressions obtained from separating the spherical components of the expanded Einstein equations and components of the gauge transformations. The notebook M2xS2-SplitcoordinatesFinal.nb takes the tensorial expressions from M2xS2-Split_Final.nb as input and expresses them in an explicit coordinate basis. This allows us to repeat the derivation of the Zerilli equation at first order and derive the Zerilli equation including its source term at second order.
All notebooks heavily rely on the xAct package for Mathematica that allows for all kinds of tensor calculations. The file M2xS2-SplitFinal.nb only works with coordinate-free tensorial quantities and as such uses the xTensor package. Both HeadOnCollissionFinal.nb and M2xS2-SplitcoordinatesFinal.nb work in explicit coordinate basis. Therefore, they require the xCoba package for calculations in a coordinate basis/chart.
Since M2xS2-SplitcoordinatesFinal.nb takes input from both M2xS2-SplitFinal.nb and HeadOnCollissionFinal.nb it is important to set up the proper kernel configuration when running the files. Make sure each file runs on a separate kernel to avoid clashes between definitions and packages and, furthermore, set all kernels to global to make sure outputs can be exchanged between notebooks.
Owner
- Login: tvdsteen
- Kind: user
- Repositories: 1
- Profile: https://github.com/tvdsteen
Citation (CITATION.cff)
cff-version: 1.0.0 message: "If you use this software cite it as below." authors: - family-names: "van der Steen" given-nemas: "Tom" - family-names: "Bonga" given-names: "Béatrice" title: "The second order Close Limit Approximation" version: 1.0.0 date-released: 2024-08-06 url: "https://github.com/tvdsteen/2nd-order-Close-Limit-Approximation"