In my general relativity class my professor derived the form of the Kruskal-Szekeres form of the Schwarzschild metric using several formulas without actually going through the algebra. I am trying to prove the answer using these formulas but I am having some trouble, especially using the Lambert W. function. In the file I have attached, you can see that equation (9) is the final result from the changes made in the previous equations. In my attempt I tried taking the derivative of the equation for 'r' and arrived at what I have shown below. However, when subbing this in and working with this I don't feel I am making progress. Any assistance is greatly appreciated, thanks.(adsbygoogle = window.adsbygoogle || []).push({});

[itex]dr=2m\frac{dL}{dz}dz[/itex]

where [itex]z=\frac{-uv}{e}[/itex]

The link for my professor's paper is at this link, http://arxiv.org/pdf/1202.0860v2.pdf , but I will also include the .pdf

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Form of Kruskal-Szekeres Completion

**Physics Forums | Science Articles, Homework Help, Discussion**