In his book (Relativity) published in 1920 Einstein said that in General Relativity the speed of light is affected by gravity and therefore isn't a constant:(adsbygoogle = window.adsbygoogle || []).push({});

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; it's results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light) - Relativity, Albert Einstein, page 64

What this means is that the speed of light that we measure with our telescopes is constant because the light is affected by our gravitational field. By the time light reaches our telescopes it enters into our gravitational field and gives us it's constant speed. We don't know the speed of light outside our gravitational field. For those who disbelieve the variable speed of light in General Relativity, taught by Einstein, here's a paper published in 2015 demonstrating a variable speed of light model consistent with General Relativity.

http://arxiv.org/pdf/1503.06763.pdf

Abstract

It is a little known fact that while he was developing his theory of general relativity, Einstein's initial idea was a variable speed of light. Indeed space-time curvature can be mimicked by a speed of light c(r) that depends on the distribution of masses. Einstein's 1911 theory was considerably improved by Robert Dicke in 1957, but only recently has the equivalence of the variable speed of light approach to the conventional formalism been demonstrated. Using Green's functions, we show that Einstein's 1911 idea can be expressed in an analytic form, similar to the Poisson equation. Using heuristic arguments, we derive a simple formula that directly relates curvature w to the local speed of light. In contrast to the conventional formulation, this allows for a Machian interpretation of general relativity and the gravitational constant G. Gravity, though described by local equations, has it's origin in all other masses in the universe.

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# Variable Speed Of Light In General Relativity

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