# Gravitational Redshift and Hubble.

1. Mar 29, 2014

### piareround

Hey guys,

I feel like an idiot for asking this. However, I wanted to make sure that my head was screwed on straight before I asked my old astronomy professor permission to use some of his old lecture notes.

Is gravitational redshift one of the causes of Hubble's Law? Is the Redshift of the hydrogen spectrum from Galaxies an example of Gravitational redshift or is it a part of that redshift?

I feel like Redshift of Galaxies is not a perfect example; however, I am not 100% sure. However, I should know this and I am kind of too embarrassed to ask my old astronomy professor.

P.S. Actually pictures/graphs would be really nice >,< (embarassed face) Does anyone know of any good pictures or graphs showing the redshift of galaxies and what part of that redshift is due to general relativity?

Last edited: Mar 29, 2014
2. Mar 29, 2014

### Staff: Mentor

No.
Gravitational redshift is there (as contribution independent from redshift from the expanding universe), but for galaxies far away this effect is negligible. And it does not depend on the distance.

You can compare the two effects via the apparent relative velocity due to the expansion (for galaxies with distances of billions of light-years, this is a significant fraction of the speed of light) to the escape velocity of those galaxies (of the order of hundreds of km/s).
Oh, and we get some blue-shift as the light enters the milky way, of course.

3. Mar 29, 2014

### Bill_K

Just for the heck of it, the formula is

$$1 + z = \frac{\lambda_{obs}}{\lambda_{em}} = \sqrt{\frac{1 + \beta}{1 - \beta}}$$
where z is the redshift, or

$$\beta = \frac{(1 + z)^2 -1}{(1 + z)^2 +1}$$

For galaxies, the greatest redshift observed is z = 12, implying β = 168/170 = 0.988.

Wikipedia claims that for the CMB, z = 1089.

4. Mar 29, 2014

### piareround

Thanks mfb, I felt kind of silly, but I wanted to confirm that the two redshifts were infact different. In fact, this helps clear up some of the confusion I had about a line from my old professor's lecture notes:
It seem like most of the test of Graviational Redshift are either ground based tests or negilible observations of the Sun -_-;
Does anyone know of any astronomical examples or pictures of Gravitational Redshift? You know where it is not negligible?

5. Mar 29, 2014

### Bill_K

Timing of pulsars, e.g. the binary pulsar. Also X-ray flares from neutron stars contain spectral lines that exhibit a significant gravitational redshift.

Last edited: Mar 29, 2014
6. Mar 30, 2014

### Staff: Mentor

In accretion disks around black holes, gravitational redshift has a huge effect.

7. Apr 6, 2014

### Ken G

The term "gravitational redshift" has always bothered me. I realize that all the responders in this thread are using the conventional meaning, that a gravitational redshift is the redshift due to the gravity of the source doing the emitting, or some other local mass concentration encountered along the way, but not the gravity of the universe as a whole on the largest scales, the latter being considered to be "cosmological redshift." But still, it seems to me that terminology fosters misconceptions and is unfortunate, albeit standard. After all, in cosmology, essentially the only thing going on is gravity-- all cosmological redshifts trace the dynamical history of the metric, and that is governed by gravity, indeed that is what gravity is in GR. So all cosmological redshifts, treated in GR, are gravitational redshifts, even though that latter term is not commonly used in that situation. Granted this is a semantic point, and the term "gravitational redshift" is almost always used the way it is in this thread, but still it is worth pointing out that they all come from the same physical source-- how gravity affects the metric that determines the wavelength of the light we observe. In particular, we can escape the common question of when does the "Hubble expansion" take over from the local gravity of individual galaxy clusters, when we recognize that it's all gravity-- all that is changing is the size scale over which the affects of the gravity are being considered.

8. Apr 6, 2014

### Drakkith

Staff Emeritus
Ken, my understanding is that gravity is caused by the warping of space, not that gravity causes the warping. If so, then you cannot call the metric expansion of space "gravity" and gravitational redshift would be an inaccurate name.

9. Apr 6, 2014

### Ken G

Do you think there is some way to tell the difference between the warping of spacetime, and gravity, such that you could make the distinction you are making here? If gravity does it, it shows up in GR, and the only other way to get a redshift is to have relative motion. There is no need to include any relative motion in cosmology, it's all just GR. Hence, all the redshifts that occur in cosmology, and also what is normally called "gravitational redshift", all come just from GR. GR is a theory of gravity, so what comes from GR, is a gravitational effect.

10. Apr 6, 2014

### Chronos

Only gravity at the emission source and observer plays any role in gravitational redshift. Photons passing through a gravity well are not affected. They are blue shifted upon entering a gravity well and redshifted upon exiting for a net zero effect. An observer in a gravity well would notice incoming photons are blue shifted. Since they do not exit the gravity well, they are unable to shed the blue shift acquired during their approach.

11. Apr 6, 2014

### Ken G

That's the conventional meaning of gravitational redshift, I'm talking about the words "gravitational redshift", which sound like they mean "redshift that exists due to gravity." Of course all cosmological redshifts are redshifts that exist because of how the universal metric evolves dynamically in time, and the universal metric is the universal version of that same local metric that you are talking about with the gravity "at the emission source." It's all GR, it's all gravity, it's all redshifts due to gravity.

12. Apr 6, 2014

### Staff: Mentor

I would say GR is more than gravity - in particular, the expansion of space does not need matter (and I would not call it an effect of gravity), but it is certainly a part of GR.

13. Apr 6, 2014

### Drakkith

Staff Emeritus
I don't agree because I don't use the word "gravity" to talk about the expansion of space. Both are the result of the geometry of spacetime, but they have very different effects.

14. Apr 6, 2014

### Mordred

The others have already answered your questions, however I regularly post this article covering the distinction between the 3 types of redshifts in cosmology. Yes gravitational redshift and cosmological redshift can be treated the same however the metrics to do so get extremely complex. You essentially have to break the redshift down in small segments to do so. Bunn and Hoggs showed this methodology. However it is far simpler to keep the 3 types of redshifts separate. Anyways here is the article I usually post lol

https://www.physicsforums.com/showpost.php?p=4687696&postcount=10

15. Apr 6, 2014

### Ken G

I have no objection to keeping the three types separate, they would almost certainly be calculated separately. My issue is with the nomenclature-- the tendency to associate only the local gravitational redshift with "gravity," and the global one with "expansion," tends to obscure the perspective that cosmology is all about gravity. We can see this perspective on this thread, as several don't view cosmological expansion as an effect of gravity. I think that's an interesting issue, what is gravity anyway?

In my view, under GR, we have a totally new perspective on gravity-- gravity is the dynamical laws that determine inertial motion. This means gravity is a modification to Newton's first law, not an aspect of Newton's second law as it used to be conveyed. Granted, if a graviton concept is successfully merged into quantum mechanics, we may go back to seeing gravity as belonging in the second law, but I don't think we're there yet. So if gravity is still in the first law at the moment, then anything that involves inertial motion, even universal expansion, is gravity.

This is not just my personal view, by the way-- even the first line in the Wiki on GR corroborates it: "General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916[1] and the current description of gravitation in modern physics." So if GR is regarded as a theory of gravity, and if the EFE is the fundamental equation of the dynamics of the universe on the largest scales, then universal expansion is best regarded as a gravitational phenomenon. I'm not saying everyone must view it that way, but I do see advantages in viewing it that way-- advantages that the nomenclature "gravitational redshift" is not particularly helpful in bringing out.

16. Apr 6, 2014

### Drakkith

Staff Emeritus
No one here has said that GR isn't a theory of gravity, only that the term "gravity" may not be the best way of describing things like the metric expansion of space. My key reason is that every time I've ever heard or used the term, it's been used to describe the way objects are attracted to other objects, never as a repulsive force. Given that gravity is the result of a curvature of spacetime due to the presence of mass and energy, while expansion is the lack of normal mass and energy, I see no compelling reason to describe expansion as being gravity.

17. Apr 6, 2014

### Mordred

Another consideration. Describe expansion as per gravity in a De-Sitter universe. This is a model that has no matter. Gravity is only one influence in the FLRW metrics. The pressure relations of the critical density is an ideal gas relation involving the energy density of the cosmological constant and matter. Universe geometry is essentually a pressure relation compared to the critical density. The energy density to pressure relation is further defined by the equations of state.

http://en.m.wikipedia.org/wiki/De_Sitter_universe

18. Apr 6, 2014

### Ken G

It is not at all uncommon to hear dark energy (or the cosmological constant) referred to as a kind of antigravity effect. It all comes back to, what is gravity? If you make gravity be just the attraction of masses and nothing else, then you have a strange situation where inertial paths are decided by gravity and something else. Since gravity isn't doing anything except contribute to the dynamical determination of inertial paths, why make such an artificial distinction?

The bottom line is, GR is a dynamical theory about inertial motion, and dark energy fits in with that. Since GR is also described as a theory of gravity, a normal conclusion is that gravity should now be considered to be the dynamical rules of inertial motion. Hence, dark energy is a form of gravity. This may not be the sole language that makes sense, but frankly I've never heard any better language for talking about the EFE. If the EFE is not gravity, then what is?

Expansion is governed by the dynamics of the curvature of spacetime. What else could determine expansion?