I know about special relativity and Lorentz transformations. However, there is also the general coordinate transformation (GCT) which is allegedly used in general theory of relativity. What is GCT and how is it different from the Lorentz transformation?
I know how do Lorentz transformations look like. I want to see how does a GCT look like. Please include that in the answer. Moreover, Lorentz transformation keeps $ds^2$ unchanged. Does GCT also keep $ds^2$ unchanged?