http://philsci-archive.pitt.edu/9825/1/Lehmkuhl_Einstein_Geometrization.pdf Why Einstein did not believe that general relativity geometrizes gravity, Dennis Lehmkuhl: "I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or (subsequently) the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity."
Then why do Einsteinians refer to geometrization of gravity any time the speed of light in a gravitational field is discussed? In order to camouflage the simple fact that the speed of light varies with the gravitational potential like the speed of any material body:
That, in a gravitational field, the speed of light varies like the speed of any material body (as predicted by Newton's emission theory of light) has been confirmed by the Pound-Rebka experiment:
http://courses.physics.illinois.edu/phys419/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."
http://www.einstein-online.info/spotlights/redshift_white_dwarfs Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."
If, in a gravitational field, the speed of light varies like the speed of any material body, then, in gravitation-free space, it varies with the speed of the observer, as predicted by Newton's emission theory of light and in violation of Einstein's relativity:
http://www.youtube.com/watch?v=FJ2SVPahBzg "The light is perceived to be falling in a gravitational field just like a mechanical object would. (...) The change in speed of light with change in height is dc/dh=g/c."
Integrating dc/dh=g/c gives:
c' = c(1 + gh/c^2)
Equivalently, in gravitation-free space where a rocket of length h accelerates with acceleration g, a light signal emitted by the front end will be perceived by an observer at the back end to have a speed:
c' = c(1 + gh/c^2) = c + v
where v is the speed the observer has at the moment of reception of the light relative to the emitter at the moment of emission. Clearly, the speed of light varies with both the gravitational potential and the speed of the observer, just as predicted by Newton's emission theory of light.