# Geodesic equations

1. Dec 15, 2009

### espen180

I tried to find the differental equations that describe geodesics in polar coordinates.

Using $$g=\left[\begin{matrix} 1 & 0 \\ 0 & r^2 \end{matrix}\right]$$ as the metric.

I did not show the steps in expanding the Christoffel symbol. There are three nonzero elements in it, simplified there are two elements (Two of the three are equal).

http://img686.imageshack.us/img686/1561/geodesic.jpg [Broken]

Where the two cases $$\lambda=1,2$$ have to hold simultaneously.

The differential equations I found here say that any path going radially outwards from the center in a geodesic, which is expected. Also, circles are not geodesics.

I guess that the only way to test the validity of the equations is to plug in a general expresssion for a straight line?

Last edited by a moderator: May 4, 2017