Dear all, First, please forgive my english, I am French. In most textbooks on general relativity (GR) the non trivial geometry is introduced in this way : the equivalence principle says that we can forget gravity as a force and consider an accelerated frame. As this frame is accelerated it is not inertial and therefore the interval (ds^2=dt^2-dx^2) is not conserved anymore (special relativity (SR) teaches us the the interval in conserved but only when going from an inertial frame to another). As the interval encodes the geometry, we see why a non-trivial (non-euclidean) geometry appears. Sounds good to me. BUT : in many course on GR, I see that people use the fact that the interval is in fact still conserved when changing frame in GR ! So, I am a bit confused... Thanks for your help !