In a gravitational field, the speed of light varies as predicted by Newton's theory:

"We conclude, therefore, that A BEAM OF LIGHT WILL ACCELERATE IN A GRAVITATIONAL FIELD AS DO OBJECTS WITH REST MASS. For example, near the surface of Earth light will fall with acceleration 9.8 m/s^2." http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf

Einstein's general relativity idiotically predicts that the speed of light falling in gravity DECREASES:

https://www.youtube.com/watch?v=FJ2SVPahBzg

"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." http://www.physlink.com/Education/AskExperts/ae13.cfm

"Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911." http://speed-of-light.com/speed_of_light_relative.html

"Thus, as φ becomes increasingly negative (i.e., as the magnitude of the potential increases), the radial "speed of light" c_r defined in terms of the Schwarzschild parameters t and r is reduced to less than the nominal value of c." https://www.mathpages.com/rr/s6-01/6-01.htm

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