I know all two dimensional metrics (in my case Lorentzian) are conformally flat, but I can't seem to prove it. I have a particularly complicated metric, and it would make my life much easier if I could transform it into coordinates in which it is conformally flat. Does anyone know the way to do this in general?
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Possible duplicate: Diffeomorphism & Weyl transformations in the 2D worldsheet of string theory and the existence of conformal gauge – Qmechanic May 25 '23 at 11:17