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Is light emitted outwards from, say, a region very close to a black hole more shifted than light with the same wavelength that began next to a less massive object?

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    $\begingroup$ It seems to me that either you have read something about "gravitational redshift", in which case, please mention the research that you've done (even if only browsing wikipedia) or you haven't, in which case this is strangely unmotivated. Please explain where you got the idea that light might be shifted at all, and by deep gravitational wells in particular. $\endgroup$ – James K Jun 28 '20 at 7:05
  • $\begingroup$ I have not read about gravitational redshift until you mentioned it. I guess the core question am am asking is whether the redshift is proportional to the time it takes to travel from the source to the viewer or the absolute distance. $\endgroup$ – dalearn Jun 28 '20 at 12:26
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Redshift is not related to the time it takes to travel from the source to the viewer, not to the distance from the source to the viewer.

But light is red-shifted by travelling out of a gravitational well. One way to see this is to consider the equivalence principle: A person at the front of an accelerating spacecraft would see light shone from the back to the front of the craft become redshifted, and would say this is due to the fact that they are moving faster when the light reaches them than when the light was emitted. If the same craft were held stationary in a gravitational field the same experiment must have the same effect, ie the light is observed to be red-shifted.

Alternately you can consider energy: If you fire a bullet vertically up, it will slow down, and lose kinetic energy as it moves out of a gravitational well. If it is travelling fast enough it might be able to escape the pull of gravity, but it will be going slower by the time it reaches a great distance.

Light, on the other hand, can't lose energy by going slower, but it does lose energy and momentum as it rises out of a gravitational well. This is seen by the photons becoming red-shifted as they rise.

Redshift can be caused by a Doppler effect (of when an object is moving away from you) or by a cosmological effect (as the space between you and the object is stretched with the expansion of the universe) or by gravitational effects as above. Redshift is not caused by the time it takes to travel from the source to the viewer. But as more distant sources are receding faster, the red-shift of more distant galaxies (that has been travelling for longer) tends to be greater.

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    $\begingroup$ Well-written; would benefit greatly if you could add quantitative examples of the relative magnitudes of red-shifting from these effects. $\endgroup$ – Carl Witthoft Jun 29 '20 at 15:06
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Not quite. Gravitational redshift is proportional to $M/R$, where $M$ is the mass interior to a radius $R$. However density $\rho$ is proportional to $M/R^3$.

So gravitational redshift does not depend directly on density. If you are considering radiation emitted from the surface of an object then the redshift is proportional to either $\rho R^2$ or $\rho^{1/3} M^{2/3}$.

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