Spinors: Spinor calculus in General Relativity

Authors: Alfonso García-Parrado and José M. Martín-García © 2007-2020 under GPL.

Article: A. García-Parrado, J. M. Martín-García, Comp. Phys. Comm. 183 (2012) 2214-2225, arXiv: 1110.2662 [gr-qc].

Introduction

Spinors is a package for spinor calculus in four dimensionali Lorentzian geometry. Some relevant features of the package are:

• Inclusion of all the quantities which are typical of the spinor calculus (antisymmetric metric, curvature spinors, 2-index covariant derivatives and more).
• Efficient tools to transform tensor into spinor expressions and back.
• Simplification of spinor expressions taking into account the specific conventions of the spinor calculus.
• Step by step derivation of all the Newman-Penrose and Geroch-Held-Penrose (GHP) equations using a combination of Spinors and other xAct packages.

See Spinors.History

Download and installation

Current version: 1.0.6 (as of 28 September 2014). It is recommended to download the main xAct bundle, but you can also download the different files separately:

• Spinors.nb: source file.
• Spinors.m: package file. This file is automatically generated by Mathematica when Spinors.nb is saved. This is the only essential file.
• SpinorsDoc.nb: main documentation file.
• PublicNPGHP.nb: explicit, step-by-step construction of the Newman-Penrose and Geroch-Held-Penrose formalisms, using the Spinors package.
• SpinorsCPCNotebook.nb: examples in the article above.
• General Public License.

See the file Spinors.readme and the Installation notes.

Previous versions:

• Spinors_1.0.5 (as of 15 February 2014).
• Spinors_1.0.4 (as of 27 January 2013).
• Spinors_1.0.3 (as of 5 May 2012).
• Spinors_1.0.2 (as of 25 October 2011).
• Spinors_1.0.1 (as of 17 April 2011).
• Spinors_1.0.0 (as of 30 September 2010).
• Spinors_0.9.2 (as of 10 January 2010).
• Spinors_0.9.1 (as of 1 December 2008).
• Spinors_0.9.0 (as of 11 August 2008).