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Since gravity curves space, I wonder how the locally increasing density of matter and energy due to the current galactic mergers with the Milky Way affects our perception of the universe.

Basically, if we have black holes coming closer to us, then the increasing curvature of space should make it look like the universe's expansion is accelerating, due to the increasing local gravitational red shift.

I'm sure I'm not the first to think of this but I wonder how well it's been studied, what the magnitude of that effect would be, and how we would even know if the curvature of space in our solar system were changing due to approaching gravitational fields.

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    $\begingroup$ Contracting or expanding space are just coordinate choices, so they don't influence physical observables. $\endgroup$
    – Sten
    Commented Mar 21 at 16:18
  • $\begingroup$ I disagree @Sten. What he mentions doesn't really have anything exactly like this in research afaik, but e.g. local density anomalies like "voids" or similarly overdensities would affect our observations. And they have been taken into considerations and studied. $\endgroup$
    – Confuse-ray30
    Commented Mar 21 at 18:32
  • $\begingroup$ @Confuse-ray30 Framing the question in terms of contracting space makes it less clear what the actual physical question is. I do not claim there is no underlying physical question. $\endgroup$
    – Sten
    Commented Mar 21 at 19:03
  • $\begingroup$ Contracting space is just the changing spacetime curvature near a large mass. "Contracting" because it's a red shift due to gravity. $\endgroup$
    – Eric Heitzman
    Commented Mar 22 at 1:03
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    $\begingroup$ So right now, we're merging with the Sagittarius Dwarf Spheroidal Galaxy, the Canis Major Dwarf Galaxy and the Large and Small Magellanic Clouds, all of which, as I understand it, have some effect on us gravitationally. That means that the curvature in our local area of space is changing (our clocks run slower, and things far away look farther away). If that's true then we should see distant things moving ever so slightly farther away. Not that they are, but our measurements are distorted by the gravitational field we are in. $\endgroup$
    – Eric Heitzman
    Commented Mar 22 at 22:20

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A back of the envelope calculation shows that the gravitational effect of the Andromeda galaxy in the vicinity of Earth is somewhat less than the gravitational effect of Alpha Centauri, which is to say, negligible. For all practical purposes the spacetime curvature here due to distant galaxies is 0.

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  • $\begingroup$ That sounds reasonable I suppose. I'm not sure how subtle the expansion discrepancy would be. And the second part of the question? If our local curvature were changing, how would we know? $\endgroup$
    – Eric Heitzman
    Commented Mar 23 at 3:56
  • $\begingroup$ If our local curvature were changing then the orbits of planets (which are following geodesics in curved spacetime) would change. $\endgroup$
    – Eric Smith
    Commented Mar 23 at 22:05
  • $\begingroup$ Possibly, but not very much if it all changed at the same time. The gradient would be pretty constant between the distant orbits and the sun. $\endgroup$
    – Eric Heitzman
    Commented Mar 24 at 0:39
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Gravitational redshift is proportional to the change of gravitational potential between where the light was emitted and where it is received.

If you were positioned in a region where the local density of mass was increasing, then this would result in a numerically decreasing gravitational redshift.

These shifts apply to all light we receive from beyond our galaxy and local group, are tiny compared with cosmological redshifts and would not produce any significant relationship between redshift and distance.

e.g., The Solar System sits in a galaxy with $M\sim 10^{11} M_\odot$ within a radius of about 8 kpc. The gravitational redshift at that position is approximately $$z \sim -\frac{GM}{Rc^2} = -6\times 10^{-6}\ ,$$ equivalent to subtracting a recession velocity of just 1.8 km/s for light entering the galaxy from outside. Adding more mass within the solar circle would increase this blue shift.

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  • $\begingroup$ So you're saying if my clock runs slower than a system emitting some light, the the light I receive is blue shifted relative to the source? Are you very sure about that? $\endgroup$
    – Eric Heitzman
    Commented Mar 23 at 10:22
  • $\begingroup$ Anyway, what we're actually interested in is the change in the curvature, taking into account the motion of the galaxies. The idea is that it might result in a small perceived acceleration of the expansion of the universe. I appreciate your calculations. Maybe there's not enough information to answer the questions if we can't measure the changes in our local curvature. $\endgroup$
    – Eric Heitzman
    Commented Mar 23 at 10:35
  • $\begingroup$ @EricHeitzman that's right. And light emitted by you, in the gravitational potential, is observed redshifted by a distant observer. Gravitational redshift is not directly related to the curvature of space or the gravitational field, it is approximately proportional to the change in gravitational potential en.wikipedia.org/wiki/Gravitational_redshift $\endgroup$
    – ProfRob
    Commented Mar 23 at 11:40
  • $\begingroup$ that's helpful. Thank you. I'll never trust ChatGPT again. :-) I get that the shift is determined by a potential, but still, how would you measure a changing potential between your frame and other distant light source? Could you expect to do it by measuring a drift in the (blue) shift? Or is it essentially unmeasurable? Gravity wave detectors measure it on a small time scale I guess. $\endgroup$
    – Eric Heitzman
    Commented Mar 23 at 13:43
  • $\begingroup$ Sounds like you are asking about redshift drift. physics.stackexchange.com/questions/170525/… @EricHeitzman $\endgroup$
    – ProfRob
    Commented Mar 23 at 13:57

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