Kerr metric derivation (Adler, Bazin & Schiffer)

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The forum discussion centers on the derivation of the Kerr metric as presented in "Introduction to General Relativity" (2nd Edition) by Adler, Bazin, and Schiffer. The user identifies a specific issue transitioning from equation (7.15b) to (7.24), particularly regarding the first term of (7.15b) and its sign. The user concludes that the first term should be negative, which resolves the discrepancy in producing the left-hand side of equation (7.24). This correction is crucial for accurate derivation in general relativity.

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seanjadson
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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(m2) equation (7.15b) to (7.24). For the first term of (7.15b) I get:

m2.lm.ln[4(A.la)|a-8A2]

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

m2.lm.ln[-6A2-2.la|b.lb|a+2.la|b.la|b]

Adding these 2 expressions does not produce a factor of the LHS of (7.24), although subtracting them does.
 
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Found my mistake; the first term should be the negative of that shown.
 

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