# Change of determinant of metric

1. Jun 21, 2014

### ChrisVer

Under a change of variables:
$x^{\mu} \rightarrow x^{\mu}+ \delta x^{\mu}$

How can I see how the determinant of the metric changes?
$\sqrt{|g(x)|}$?

Is it correct to see it as a function?
$f(x) \rightarrow f(x+ \delta x) = f(x) + \delta x^{\mu} \partial_{\mu} f(x)$
?

2. Jun 21, 2014