As I understand in SR light is always c in it's local reference frame regardless of a present gravitational field. Light would appear to be traveling slightly less than c in a gravitational field otherwise known as the Sharpio Delay in all non-local reference frames. Now, light must be traveling at c in the local reference frames to preserve causality as a consequence of SR. However, since we cannot measure light in any local reference frame is it not possible that it may be traveling less than c due to the gravitational field and s-t diagrams could be re-written to prevent any breaking of causality? If so what could the consequences be?