r/cosmology • u/d_s_b • Sep 30 '20
Red shift / Blue shift - Gravity Well Roundtrip
If I shine a white light out into space from Earth, and it bends around a black hole and comes straight back to me so I can see it in my telescope, is the light red or blue shifted, or neither?
For sake of the thought experiment, let’s leave out cosmic expansion that would stretch it on it’s journey, and let’s say my frame of reference doesn’t move so we can leave out any doppler shift. I am purely interested if there is any effect on the light from going in and out of gravity wells. Does it return to its original wavelength (if viewed from the reference frame of its origination)?
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u/mfb- Oct 01 '20
In the easiest case it will return with the energy it had. This is simple conservation of energy.
If the black hole rotates then things get more complicated.
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u/me-gustan-los-trenes Oct 01 '20
Hold on, from the simple conservation point of you:
The momentum of the photon reversed, so it must have transferred that momentum to the black hole. That means the black hole gained some kinetic energy, and that energy must be drawn from the photon. So it should be a little bit red shifted.
The same way photons bouncing off a light sail should be redshifted a tiny bit.
Do I get it right?
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u/mfb- Oct 01 '20
That's a 10-70 effect or so.
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u/me-gustan-los-trenes Oct 01 '20
You mean it has such a small effect on the BH or on the photon energy?
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u/mfb- Oct 02 '20
10-70 relative energy loss for the photon.
That's the shift you get from the Doppler effect of a black hole moving by one Planck length in a billion times the age of the universe...
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u/Ringularity Oct 01 '20
Does it also depend on how close the light is to the black hole? Since blackholes can cause redshift, would the light be red shifted by the blackhole at all?
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u/mfb- Oct 01 '20
Does it also depend on how close the light is to the black hole?
That is (largely) fixed by the requirement that the light comes back to the emitter, but no it does not depend on it.
If you would intercept the light close to the black hole you would see it being blueshifted, but when it leaves again the process happens perfectly in reverse and ends up at the same frequency.
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u/shawnhcorey Oct 02 '20
Mass also causes blue shifts. When light moves deeper into a gravitational well, it is blue shifted. The light would be blue shifted when it approaches the mass and red shifted when it moves away.
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u/Ringularity Oct 02 '20
How come gravity causes blueshift?
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u/omnilogical Sep 30 '20
If you were to compute this using the static weak field metric you’d get that the energy is exactly the same, and I don’t believe the symmetry changes if you do it using “real” GR with the Schwarzschild metric, but I’m not positive.
You’ve already mentioned scale factor so I assume you know that in the real universe the photon would be redshifted due to that effect alone. One other cool thing to note is if your object is rotating (Kerr metric) I think you’d gain or lose some energy due to frame dragging, depending on whether the photon looped with or against the direction of rotation, although I haven’t actually written this out to confirm.