I have very little knowledge in general relativity, though I do have a decent understanding of the theory of special relativity. In special relativity, points in space-time can be represented in Minkowski space (or a hyperbolic space) so that the metric tensor (that is derived in order to preserve the invariant interval) has a unique form corresponding to that space. From what I understand (and I say this with caution as I could easily be mistaken), since in the theory of general relativity light bends under the influence of gravity (does it?), this requires a more complicated set of coordinates hence the use of more complicated metric tensors to preserve the invariant interval in such curvilinear space. Is that correct? how would such metric tensor look like?