Find Null Geodesics with affine parameter

[myra2016]

Homework Statement

The metric is given by
https://dl.dropboxusercontent.com/u/86990331/metric12334.jpg
H is constant; s is an affine parameter, and so r(0)=t(0)=0.

Apologise in advance because I'm not very good with LaTex. So I used Word for equations, and upload handwritten attempt at solution

Homework Equations

Need to show that the null geodesics from r=0, t=0 are given by
https://dl.dropboxusercontent.com/u/86990331/metricquestion.jpg

The Attempt at a Solution

I get the required t but the sign is different.
https://dl.dropboxusercontent.com/u/86990331/metricattemptatsolution.jpg

 

[Shostakovich]

Hello, please attempt to re-upload the images, currently the links appear to be broken and may very well be the reason no one can help.