I tried to find the differental equations that describe geodesics in polar coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

Using [tex]g=\left[\begin{matrix} 1 & 0 \\ 0 & r^2 \end{matrix}\right][/tex] 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 [tex]\lambda=1,2[/tex] 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?

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# Geodesic equations

Can you offer guidance or do you also need help?

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