Mathematica-in-GR-and-Cosmology

In this repository, I'm going to solve examples of GR and Cosmology using Mathematica. The main package in my work is xAct, but I'll use other packages too. For using xAct, you have to add this library to your Mathematica software (I supposed you have installed Mathematica already!). You can use below link for installtion notes of this package: http://www.xact.es

Notes:

• For getting the complete vesrion of a specific code, please right click on it and hit 'save link as' to download that.

• The full explanation of examples, is above them.

• My Mathematica's vesrion is 12.1

• Mathematica's notation is in according to Wald's book

• if you found any errors, don't hesitate to contact me

Examples

1. All you need in polar coordinate is here!! (including Christoffel symbols and Riemanian tensors) polar_coordinate.nb
2. All you need in semilog coordinate is here!! (including Christoffel symbols and Riemanian tensors) semilog_coordinate.nb
3. All you need for a 2D sphere is here! (including Christoffel symbols, Riemanian tensors, Ricci tensor and scalar) 2D_sphere.nb
4. All you need for a solid sphere is here! (including Christoffel symbols, Riemanian tensors) solid_sphere.nb
5. The first steps of deriving Schwarzschild metric (this section is adapted from the Thomas A.Moore's book) derivation_of_the_Schwarzschild_metric.nb