So I was wondering about the event horizon on a black hole. And wondering if the

Question

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?

Explanation / Answer

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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