Basically I am asking if gravitional lensing is bending or refracting light.
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2 Answers
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The equivalence principle says yes. Consider an elevator accelerating upward in flat spacetime and a horizontal light ray entering from one side. To an observer in the accelerating elevator, the light ray will appear to curve downward and hit a lower point on the opposite wall. To an inertial observer the light ray follows a straight path. All light rays follow a straight path in flat spacetime regardless of frequency, so the amount of bending seen by the accelerating observer is unaffected by the frequency of the light ray. If light rays of different frequencies followed different curved paths from the accelerated observer's point of view, then they would have to follow different curved paths in flat space time for no good reason, because there is no gravity acting on them. This principle is at the very heart of general relativity. This 'refraction' of light rays by a gravitational field is different to the regular refraction of light by an optical medium where the path is different for different frequencies.
P.S. Gravitational lensing has not been observed to produce rainbows.
P.P.S. As John Doty points out in the comments there may be outliers and subtleties in extreme cases. One example I can think of is that normal visible light travelling straight from the source to the observer can be blocked by any intervening gravitational lensing body, while x-rays might pass pass straight through the body.
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Does gravitational lensing bend light of all wavelengths by the same amount?
Yes it does. All light, regardless of wavelength follows the same path called a null geodesic. In fact any massless particle would also follow the same path.
answered Feb 18 at 15:04
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$\begingroup$ As long as the ray approximation holds. But, in theory, for wavelengths comparable to the lens dimensions, there'll be diffraction, and for wavelengths much longer the lens will have little effect. $\endgroup$ Commented Feb 18 at 15:24
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$\begingroup$ Wouldn't a high energy photon have more effect on the spacetime curvature along its path and thus follow somewhat different null geodesics compared to a low energy photon? $\endgroup$ Commented Feb 18 at 19:11
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$\begingroup$ @user10001 if the total energy density of the light beam gets high enough it could cause a significant curvature, but a single photon is not going to do it. The total energy of the beam could be lots of low energy photons or fewer high energy photons and the end result would be the same. $\endgroup$ Commented Feb 18 at 20:14