Gravity and speed of light

Abstract

One of the postulates of the Special Theory of Relativity is that the speed of light is constant
in all inertial reference frames regardless of the motion of the observer or source. This postulate also apply to the General Theory of Relativity.
There are many experiments whose results are consistent with the assumption that gravity does not affect the speed of light. But notwithstanding all this we may argue
that it has not been formally proved. One way to prove its correctness is to replace it with the opposite axiom, axiom of variable speed of light. If there is at least one experiment
whose result would possibly be in contradiction with this axiom, then it must be rejected and the axiom of a constant speed of light must be accepted.