I will only care about the ##t## and ##x## coordinates so that ##(t, z, x, x_i) \rightarrow (t,x)##.
The normal vector is given by,
##n^\mu = g^{\mu\nu} \partial_\nu S ##
How do I calculate ##n^\mu## in terms of ##U## given that the surface is written in terms of ##t## and ##x##?
Also, after...