So far our discussion of gravity has been completely non-relativistic. We will not explore in detail how the theory of gravity changes in a completely relativistic treatment. As we noted earlier in the course, Einstein's general theory of relativity covers this, and the mathematics are formidable. As noted previously, gravity is locally equivalent to being in an accelerated reference frame. However, unlike the simple example which we studied earlier, there is in general no universal frame of reference to which we can transform which is everywhere inertial.
Space is even more non-Euclidean in general relativity than in special relativity.
In particular, there is no such thing as a straight line in the geometry of general relativistic spacetime. This is true because spacetime itself is curved. An example of a curved space is the surface of a sphere. Clearly, a straight line cannot be embedded in this space. The closest equivalent to a straight line in this geometry is a great circle.