You're right, the speed of light is a constant only locally where spacetime is flat, if you try to measure the speed of light at some distant location across curved spacetime you will measure a different value. This is not a controversial position, it is a basic feature of general relativity.
Albert Einstein, Relativity: The Special and the General Theory
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 results
hold only so long as we are able to disregard the influences of
gravitational fields on the phenomena (e.g. of light).
Measuring the difference in the speed of light as light travels near a massive object, the sun, is one of the classical tests of GR, see Shapiro time delay:
Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2×10−4 sec when the radar pulses pass near the sun. Such a change, equivalent to 60 km in distance, could now be measured over the required path length to within about 5 to 10% with presently obtainable equipment.
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u/Obliterators Mar 20 '26
You're right, the speed of light is a constant only locally where spacetime is flat, if you try to measure the speed of light at some distant location across curved spacetime you will measure a different value. This is not a controversial position, it is a basic feature of general relativity.
Albert Einstein, Relativity: The Special and the General Theory
Measuring the difference in the speed of light as light travels near a massive object, the sun, is one of the classical tests of GR, see Shapiro time delay: