Ricci tensor equation

  • Thread starter Lapidus
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In Zee's "Einstein's Gravity in a Nutshell" on page 363, while deriving the Schwarzschild solution, we have
upload_2015-1-3_0-14-7.png


How does it work? How are the rhs and lhs equal? Where does the factor 2 come from, why just one derivative left?

thanks for any replies!
 

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  • #2
Orodruin
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The solution is assumed independent of the t-coordinate so derivatives wrt that coordinate vanish. The 2 appears because you have the possibilities if sigma and kappa taking values r and t in tha term. This can be done in two ways.
 
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