http://bartleby.net/173/22.html Albert Einstein: "In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its result hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)."
Einstein is lying blatantly here. It is easy to show that, if the speed of light "varies with position" in a gravitational field, then it varies with the speed of the observer in gravitation-free space, in violation of special relativity.
Consider falling light: since the speed of light "varies with position", we have a shift in frequency:
http://courses.physics.illinois.edu/phys419/sp2013/Lectures/l13.pdf University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light."
But the frequency shift measured by a stationary observer in a gravitational field is equivalent to the frequency shift measured by a moving observer in gravitation-free space (a fact often used in textbooks). Accordingly, if the speed of light relative to the former observer differs from c (and this causes the gravitational frequency shift), then it differs from c relative to the latter observer as well (this causes the Doppler frequency shift), in violation of special relativity.