Does the density of a galaxy affect time?

Question

Can denser galaxies appear blue shifted?

Can galaxies with different densities then our own galaxy appear blue or red shifted from movement when in fact it could be from the time dilation from density as well?

Answer 1

The answer is yes they can but the effect is trivially small.

Observed gravitational redshift just depends on the difference in gravitational potential between source and observer. Roughly, $$ z \sim \frac{\Delta \Phi}{c^2}.$$ Density is is only indirectly involved in the sense that high density regions can produce large gravitational potentials. In principle, $\Delta \Phi$ could be positive or negative resulting in red- or blue-shifts respectively.

However, as I demonstrated for this very closely related (duplicate) question Can a photon that is emitted from a denser part of the universe to a less dense part appear redshifted? the size of the effect is tiny compared to redshift caused by the expansion of the universe.

Some examples: If we consider the potential at the Earth's surface compared to intergalactic space, we can add the potentials due to the Earth, due to the Sun and due to the Galaxy (assuming $10^{11}$ solar masses within the Sun's 8kpc orbit). These terms give (additive) redshifts of $z= 4\times 10^{-10}$, $10^{-8}$ and $6\times 10^{-7}$, corresponding to a blue-shift for light arriving at the Earth, expressed as a velocity, of 0.2 km/s.

Of course the emitting regions of an external galaxy sit in their own potentials and the redshifts due to these would have to be subtracted from the number above. Such numbers are negligible compared to the hundreds of km/s that even local galaxies move with respect to the Earth.

The only exception to the negligibility of this effect would be if we specifically looked at light coming from very close to a central black hole. For example X-ray emission of gas in active galactic nuclei emitting light from close the innermost stable orbit will have an observed redshift of up to about 0.2 (60,000 km/s), but such large redshifts are not used or quoted as the redshift of the galaxy that hosts the black hole.

Answer 2

The question may be a little ambiguous, as it's not clear whether whatever mass might be contained in the black hole at (or forming) the center of most galaxies is to be included in the mass whose density is under consideration: In Hawking's 2014 conclusion that the horizons of black holes are "only 'apparent'", it would be, but in the more classical formulations that they are not, it wouldn't, as the causal separation they represent would be quasi-infinite (i.e., infinite to the future) in its duration. If there's a convention for dealing with the resulting ambiguity, I'm not aware of it, although the conventional refusal to consider the "singularity" (once generally considered to lie within each BH) as explaining the externally paradoxical combination of infinite density with zero volume tends to suggest that there isn't one, in which case I'd assume the overall galactic density inward from the outer surface of a galaxy centered around a particularly large central BH to be relatively low compared to the density of those lacking any BH fitting that description, as the coalescence of collapsed stellar masses (ordinary BHs) into any large BH at its center would tend to be leaving the galaxy centered around it rather impoverished as to mass density, even though it would generally tend to have previously included even more binary pairs than most galaxies are assumed to have, under the usual assumption that BHs result almost entirely from the gravitational collapse of unusually large stars within such pairs, prior to whatever coalescences of them with each other may occur.

It does appear that time dilation is considered to occur regardless of causal separations, presumably because the causality on opposite sides of such separations remains common to each of them even after the gravitational collapse (due to exhaustion of stellar "fuel") that increases the scale of the escape velocity of light (to a level beyond that prevalent prior to the separation), from the gravitational (AKA "event") horizon (i.e., the location of the former stellar surface), has occurred.

The simplest post-2009 resolution of the disparity between density and volume in the so-called singularity might be Poplawski's "cosmology with torsion" (to use the title of one of his arxiv papers on the issue), which utilizes a hypothetical spin-spin interaction between stellar fermions (assumed, per the Einstein-Cartan gravity he uses, to each have a tiny spatial extent) and newer ones, separated by the event horizon from their previous partners (in virtual pairs) during tidal effects of the parenting star's gravitational collapse. The resulting and smaller-scaled "baby universe" would form on the inward side of that horizon, but would not extend permanently beyond the eventual spacetime location of still smaller ones, forming through the same process in what appears to be the "block universe" version of time: Each such iteration would, rather, be analogous to the skin of a basketball.