I have a question related to the calculation of curvature using exterior differential forms (Misner, pp. 354-363). In all the examples given in the book (i.e. Friedmann, Schwarzschild, pulsating star metrics), the "guess and check" method used to find the connection forms (Eq. (14.31)) work well because the metric has only diagonal terms [tex]g_{nn}[/tex], so an orthonormal basis such as the one given in Eq. (1) in Box 14.5 (p. 355) can be derived in a straightforward manner from the components of the metric.

Now is there any chance to apply this method when there are also off-diagonal terms ([tex]g_{mn}, m \neq n[/tex]), or is one then compelled to use the systematic way (Eq. (14.32) and (14.33)) ?

Thanks a lot for your help!