How many degrees of freedom to diagonalize the metric?
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In A. Zee's Einstein Gravity in a Nutshell , he starts with the following expansion of the metric at some point of a Riemannian manifold, with coordinates that have the origin at P : ⬆⬆
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the discover went under this formula
gμν(x)=gμν(0)+Aμν,λxλ+Bμν,λσxλxσ+...gμν(x)=gμν(0)+Aμν,λxλ+Bμν,λσxλxσ+...
gμν(x)=gμν(0)+Aμν,λxλ+Bμν,λσxλxσ+...gμν(x)=gμν(0)+Aμν,λxλ+Bμν,λσxλxσ+...
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