espen180
Dec15-09, 01:12 PM
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
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?
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
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?