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So I was wondering about the event horizon on a black hole. And wondering if the point of no return for radio waves vs gamma rays would be different. I guess the logic being, since gamma rays have more energy than radio waves, their point of no return might be different.

But I'm not sure if gravity has the same affect on all frequencies of electromagnetic radiation.

I'm sure the answer for this would lie in gravitational lensing, ie are different colours of light lensed by the same amount? or do higher frequencies lens less?

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No, there's no detectable dispersion in gravitational lensing, at least not when the wavelength is much shorter than the curvature radius.

The reason is simple to see: one may approximate the light by rays propagating along geodesics. They have to be null geodesics because the photons are massless. And given the location of the source and initial direction, such a null geodesic is unique and therefore independent of the frequency. Every photon has to propagate along the same path.

There may be tiny, practically invisible effects that correct this independence when the wavelength becomes comparable to the curvature radius.

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  • $\begingroup$ Interesting and intriguing remark (+1). That tiny effects possibility is extremely interesting for me. Have you done any back-of-the-envelope order of magnitude estimates for a realistic (although probably rare) scenario? $\endgroup$
    – Eduardo Guerras Valera
    Commented Dec 16, 2012 at 23:41
  • $\begingroup$ Question based on Lubos Moti's answer: How can photons be massless when they are impacted by gravitational lensing? Gravitational lensing is an impact of the bending of space. But that would imply that dark matter does not travel in space-time. But then it would have to follow some other gravitational law than the bending of space time. $\endgroup$
    – David Urry
    Commented Dec 12, 2022 at 0:03
  • $\begingroup$ By the equivalence principle, objects in gravitational fields freely move along universal trajectories that do not depend on the mass, just the initial place and speed. On top of that, the total relativistic mass of a photon is positive, proportional to the energy. Only the rest mass is zero. You may say that the gravitational force is small when an object is light but it is also easier to accelerate it because the inertial mass is equally low. $\endgroup$
    – Luboš Motl
    Commented Dec 13, 2022 at 4:57

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