I have a problem understanding part of Adler, Bazin and Schiffer's (Introduction to General Relativity 2nd Edition) derivation of the Kerr metric. I would be grateful if someone could explain where I am going wrong. My problem concerns the transition from the O(m(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}) equation (7.15b) to (7.24). For the first term of (7.15b) I get:

m^{2}.l_{m}.l_{n}[4(A.l^{a})_{|a}-8A^{2}]

while for the second term (INCLUDING the minus sign preceding the 2 Minkowski metrics):

m^{2}.l_{m}.l_{n}[-6A^{2}-2.l^{a}_{|b}.l^{b}_{|a}+2.l^{a}_{|b}.l_{a}^{|b}]

Adding these 2 expressions does not produce a factor of the LHS of (7.24), although subtracting them does.

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# Kerr metric derivation (Adler, Bazin & Schiffer)

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