In the general theory of relativity, the speed of light in vacuum is $c$ locally. In the special theory of relativity, a postulate is made that the speed of light is the same (called $c$) in all inertial frames.
Consider the following statement:
"The speed of light is c$c$ in all inertial frames but it can vary (even locally) in accelerating frames."
My question is:
Does this statement violate the principle of equivalence or the special theory of relativity or any fundamental law of physics?