Schwarzschild Metric - Rindler coordinates

[aCHCa]

Hello, well I just read a paper by Atish Dabholkar and Ashoke Sen, titled "Quantum Black Holes", pp. 4-5 as shown below

http://i677.photobucket.com/albums/vv140/flinnradj/Premade%20DP/1PF.jpg

http://i677.photobucket.com/albums/vv140/flinnradj/Premade%20DP/2pf-1.jpg

and I tried to find d\xi^{2}\frac{2GM}{\xi}=d\rho^{2} like this

http://i677.photobucket.com/albums/vv140/flinnradj/Premade%20DP/3pf-1.jpg

which is different from the eq. in the paper.

So, could somebody please help me to find my mistake in the calculation? Thank you

[Bill_K]

ρ2 = 8GM ξ
ρ = √8GM √ξ
dρ = √8GM ½dξ/√ξ = √2GM dξ/√ξ
dρ2 = 2GM dξ2/ξ

[aCHCa]

Ah thank you so much :D