Metric component confusion

[vizart]

I am reading a paper and the authors read the tt component of the metric from the line element ds^2=f(r)[g(r) dt^2+h(r) dr^2] as g_{tt}=g(r) instead of (what I expect to be) g_{tt}=f(r) g(r)

Could somebody please explain to me why? Thank you.

[George Jones]

This seems strange. What is the paper?