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.
Ninetrees (2020). Christoffel symbols and geodesics, symbolic model (https://www.mathworks.com/matlabcentral/fileexchange/45901-christoffel-symbols-and-geodesics-symbolic-model), MATLAB Central File Exchange. Retrieved .
Updated to include Symbolic Math Toolbox
Included reference to Mathcad equivalent file.
Edited description for display, not for content.