Example xAct notebooks with common usage patterns
Switch branches/tags
Nothing to show
Clone or download
Permalink
Failed to load latest commit information.
ActionVariation_Metric_Fields.nb Added Wrapper for VarD xPert combination which does action variation (#3 Mar 26, 2018
Angular-integration.nb Re-executed notebooks and turned TrackCellChangeTimes->False in one. Aug 24, 2013
Bianchi_I_xCoba.nb Master (#15) Mar 29, 2018
CTensorChangeCoords.nb Added a couple of new examples. Updated description of README.md. May 31, 2018
Clifford_Algebra_Traces.nb Added Clifford_Algebra_Traces.nb to show how Dirac matrices traces ca… Apr 9, 2018
ConformalEinsteinEqs.nb Added new examples: Mar 28, 2018
Conformal_Transformation.nb Master (#12) Mar 28, 2018
EB-decomp-and-3+1-split.nb File name changes Mar 30, 2018
EDGB-and-DCS-EOMs-and-C-tensors-simplified.nb Added Wrapper for VarD xPert combination which does action variation (#3 Mar 26, 2018
FriedmannLemaitreMetric_CoordinatesApproach_xCoba.nb File name changes Mar 30, 2018
Gamma matrices (Dirac algebra).nb Add example on Gamma matrices Mar 30, 2018
KerrMetric.nb Added a couple of new examples. Updated description of README.md. May 31, 2018
Lagrangian-variation-xPert-VarD.nb Re-executed notebooks and turned TrackCellChangeTimes->False in one. Aug 24, 2013
README.md Added a couple of new examples. Updated description of README.md. May 31, 2018
Raychaudhuri.nb Added Wrapper for VarD xPert combination which does action variation (#3 Mar 26, 2018
Schwarzschild_Metric_Birkhoff_Theorem.nb Modified Change of coordinates in SZ example Apr 2, 2018
SymManipulatorLovelockExample.nb Spinor methods for Lovelock tensor Mar 25, 2018
TimelikeCongruence.nb Don't need execute bit on notebook Mar 30, 2018
Warped-product.nb Added warped product example Apr 24, 2014

README.md

Example xAct notebooks

This is a collection of example xAct notebooks that contain common xAct usage patterns. Right click on a file name below and hit "Save link as..." to download a notebook.

ActionVariation_Metric_Fields.nb: General function to vary a Lagrangian

Angular-integration.nb: Example of angular integration on multiple direction vectors (adapted from Post-Newtonian computations)

Bianchi_I_xCoba.nb: Bianchi I Einstein equation using the CTensor framework of xCoba

Clifford_Algebra_Traces.nb: Clifford algebra construction in all integer dimensions and fast evaluations of traces of products of Dirac matrices. The tracing function is applied to weak-interaction reaction rates.

ConformalEinsteinEqs.nb: Implementation of the Friedrich's conformal field equations in dimension 4 (metric equations and extended equations).

Conformal_Transformation.nb: Tools to perform conformal transformations and examples. Adapted from a subpart of xPand's code.

CTensorChangeCoords.nb: Simple example of coordinate change using the CTensor framework.

EB-decomp-and-3+1-split.nb: Examples of 3+1 decomposition applied to the Weyl tensor

EDGB-and-DCS-EOMs-and-C-tensors-simplified.nb: Getting equations of motion and simplifying "C-tensors" for Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons theories

FriedmannLemaitreMetric_CoordinatesApproach_xCoba.nb: It shows how to define charts and specify the components of the metric so as to obtain the components of the related curvature tensors. Shows also how to change between different charts. Applied to homogeneous cosmology.

Gamma matrices (Dirac algebra).nb: How to treat the algebra of gamma matrices with DefProduct, and canonicalize them to derive many standard identities.

KerrMetric.nb: Some computations for the Kerr metric in Boyer Lindqvist coordinates and the null tetrad. Computation of the surface gravity.

Lagrangian-variation-xPert-VarD.nb: A common usage pattern for varying a Lagrangian with respect to the metric to get Einstein equations

Raychaudhuri.nb: Follows section 9.2 of Wald's book (General Relativity) on the Raychaudhuri equation for a congruence of timelike geodesics

SymManipulatorLovelockExample.nb: Application of the Spinors and SymManipulator package to show the Lovelock tensor is non-dynamical.

Schwarzschild_Metric_Birkhoff_Theorem.nb: Construction of the Schwarzschild metric. Eddington Finkelstein coordinates and surface gravity as simple applications of the CTensor tools of xCoba.

TimelikeCongruence.nb: 1+3 decomposition of the Ricci and Bianchi identities in dimension 4 with respect to an arbitrary unit timelike vector field. The kinematical quantities and the spatial parts of the Riemann tensor are used to obtain the decompositions.

Warped-product.nb: Minimal example 1) creating a warped product geometry and 2) breaking down the Einstein-Hilbert Lagrangian into the effective lower-dimensional Lagrangian.