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Christoffel symbols and geodesics, symbolic model

version 1.3.0.0 (6.11 KB) by Ninetrees
Uses MATLAB symbolic processor to produce symbols

5 Downloads

Updated 28 Mar 2014

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This is a MATLAB document to symbolically compute Christoffel symbols and geodesic equations, using a given metric gαβ. Justification for the method is found in various texts on general relativity, and is not duplicated here. By working through Lagrange's equations for the line element of a given metric, such as the wormhole metric,
ds^2 = -dt^2 +dr^2 + (b^2 + r^2) * (dΘ^2 + sin^2 (Θ) dΦ^2)
a general expression for the Christoffel symbols of the metric and its derivatives is obtained. Though this illustrates the use of MATLAB, it is more educational than functional. Nonetheless, Gamma /is/ the MDA of Christoffel symbols for this metric, and the geodesic, however plainly displayed, is complete.
This script contains comments for those coming to MATLAB from other platforms.
I posted a Mathcad version of this on the PTC forum (web search), along with the MATLAB code (by request). My purpose is to make the material available to a wider audience.

Comments and Ratings (1)

You should select the Symbolic Math Toolbox tag in the "Required Products" field since the user also needs it.

Updates

1.3.0.0

Updated to include Symbolic Math Toolbox

1.2.0.0

Included reference to Mathcad equivalent file.

1.1.0.0

Edited description for display, not for content.

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux