The following texts are not just perplexing - they paralyze Einsteinians:

https://archive.org/stream/EinsteinR...ought_djvu.txt
Albert Einstein: "Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable."

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."

Yes, according to Einstein's general relativity, the speed of light falling towards the source of gravity DECREASES (in the gravitational field of the Earth the acceleration of falling photons is -2g). This is idiotic isn't it:

http://www.physlink.com/Education/AskExperts/ae13.cfm
"Contrary to intuition, the speed of light (properly defined) decreases as the black hole is approached. (...) If the photon, the 'particle' of light, is thought of as behaving like a massive object, it would indeed be accelerated to higher speeds as it falls toward a black hole. However, the photon has no mass and so behaves in a manner that is not intuitively obvious. (....) When we say that the speed of light is decreased, we mean from the perspective of an observer fixed relative to the black hole and at an essentially infinite distance. On the contrary, to an observer free falling into the black hole, the speed of light, measured locally, would be unaltered from the standard value of c. Most of us have heard of the result from special relativity that the speed of light is the same for all observers in inertial frames. The result is not the same in general relativity. In general relativity, the statement becomes that the speed of light is the same (i.e., good old 'c') for all observers in local inertial frames. Local inertial frames in general relativity are just those frames of reference in which the observer is in gravitational free fall. (...) So, it is absolutely true that the speed of light is not constant in a gravitational field [which, by the equivalence principle, applies as well to accelerating (non-inertial) frames of reference]. (...) Indeed, this is exactly how Einstein did the calculation in: "On the Influence of Gravitation on the Propagation of Light," Annalen der Physik, 35, 1911, which predated the full formal development of general relativity by about four years. This paper is widely available in English. You can find a copy beginning on page 99 of the Dover book "The Principle of Relativity." You will find in section 3 of that paper, Einstein's derivation of the (variable) speed of light in a gravitational potential, eqn (3). The result is, c'=c0(1+V/c^2), where V is the gravitational potential relative to the point where the speed of light c0 is measured. You can find a more sophisticated result derived later by Einstein from the full general theory in the weak field approximation in the book: 'The Meaning of Relativity,' A. Einstein, Princeton University Press (1955). See pp. 92-93, eqn (107)." x

http://www.speed-light.info/speed_of_light_variable.htm
"Einstein wrote this paper in 1911 in German. (...) ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+φ/c^2) where φ is the gravitational potential relative to the point where the speed of light c0 is measured. Simply put: Light appears to travel slower in stronger gravitational fields (near bigger mass). (...) You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911." x

http://www.mathpages.com/rr/s6-01/6-01.htm
"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential φ would be c(1+φ/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+φ. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. (...) ...we have c_r =1+2φ, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term." x

Pentcho Valev