Einstein's special theory of relativity predicts that nothing can exceed the speed of light. But special relativity applies when spacetime is flat. When spacetime is curved, the theory applies only "locally"--that is, over regions of spacetime small enough to be considered flat. Consider the analogy of a plane that is tangent to a sphere. The flat geometry of the plane is a good approximation to the geometry of the sphere when the size of the plane is very small compared to the sphere's radius of curvature.
