After using Simplify the indices are are arranged in the tensor. I am using the April 14th update from the Physics R&D page.

(1) 

(2) 

(3) 

(4) 

(5) 
We first define the Christoffel symbol in terms of the metric, .

(6) 

(7) 

(8) 

(9) 

(10) 
Now we can substitute into the null condition for the Ricci tensor, .

(11) 

(12) 
Do the first term

(13) 

(14) 
Do same thing with the first term but use the Simplify command

(15) 

(16) 
Simplify command does make the algebra easier, but the indices are not the same. Now, equation 16 should correspond to equation 14, but there is no combination of alphas that is consistent. The variables alpha1 and alpha5 must be rho. One term is always wrong when I try to change the other indices.
alpha2 and alpha3 must be either mu or nu based on the first term. But alpha6 should also be either mu or nu based on the last term, however that will make alpha2 and alpha3 either (nu and rho) or (mu and rho). Neither combination makes all of the terms consistent with (14). Very frustrating.

(17) 

Download Vacuum_Solutions_(KerrSchild)_3.mw
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