Rolando

We would not see it reach the event horizon since, from our perspective, this would take an eternity. I have neither a clear understanding of quasars nor any problem with the fact that we can see them. The orbit at which light will circle the black hole forever is, in fact, outside the event horizon. Such orbits exist already for objects that are not quite as extreme as black holes and whose possible existence my reasoning does not deny. We actually won't see anything, because of the infinte time dilation (= infinite redshift).

Even here, I expressed myself unclearly. I just meant that time dilation affects everyting that is in the same state of motion in the same gravitational well to the same extent. However, we will have to wait for an eternity until we cannot see "them" at all.

Right, I meant even here the observer's time. Anything slows down. Yes. To my knowledge, the compact objects that have actually been observed directly are all bright.

Considering the answers by imatfaal as well as by Arch2008 and Airbrush, so far, my understanding is this: A black hole is an object whose mass is hidden behind an event horizon. The event horizon represents a boundary at which time is "frozen", i.e., infinitely dilated, as seen by a distant observer. This implies that it will take light (or any signal) emitted at the event horizon an eternity (= infinite time) to reach a distant observer. It also implies that material that falls towards the event horizon needs an eternity in order to reach it (as seen by the distant observer). From this, I have to conclude that black holes cannot arise in a Universe that has only been in existence for a finite time (and it is questionable whether they could in an eternal Universe). There is no doubt about the existence of objects such as collapsed stars and galactic nuclei with very deep gravitational wells, which cause a very substantial time dilation and redshift, and infall phenomena of various kinds, but these objects are not "black holes".

imatfal - I do not see any disagreement with what you are telling, but I do not understand why you choose to consider an outside accelerated reference frame. What you say holds also for an outside stationary frame. You said that time dilates to such an extent that objects falling into the black hole seem to freeze at the event horizon. This just agrees with what I expressed in other words. Compared with an observer's time, this frozen time is infinitely dilated.

This sentence was: "Thus, in the observer's frame of reference, event horizons are at an infinite distance in time." Let me paraphrase it: "Thus, in an astronomer's frame of reference, event horizons are infintly remote in time, i.e., due to time dilation, it would take an eternity for light or any kind of signal to reach us from a position at the event horizon."

There is enough time for a star to collapse into a state in which its density perhaps even exceeds that of a neutron star, but this is not yet a black hole. As seen by a distant observer, it takes an eternity for the collapsing material to reach the event horizon.

According to my understanding, a black hole is defined as an object whose mass is hidden behind an event horizon. According to its definition, an event horizon represents a boundary from which it takes an infinite time for light to reach a distant observer. Thus, in the observer's frame of reference, event horizons are at an infinite distance in time. Now, current doctrine teaches us that there are black holes in the Universe while it also teaches us that the Universe has existed for only a finite time. To me, it is obvious that these teachings contradict each other, yet I have seen them repeated over and over again also in the most prestigious publications. How can this be?

You are basically right, but the problem exists in both alternatives (as you seem to imply yourself). In the contraction alternative, proportionality within gravitationally bound systems is not the problem, but in order to calculate the distances between galaxies that are not gravitationally bound to each other, some points have to be considered as central.

There are some among the references in L Marmet's draft "On the interpretation of red-shifts: A quantitative comparison of red-shift mechanisms" (http://www.marmet.or.../mechanisms.pdf)

I do not think of a centre. We can consider gravitationally bound systems as stable and the regions between them as expanding. We can also consider gravitationally bound systems and everything within them as contracting and the regions between them as stable. The Universe looks the same in these cases.

It does not look like a collapse when everything shrinks in proportion. Within stable gravitationally bound systems, blueshifts will be as common as redshifts. It does not tell anything about redshifts between clusters. Thank you for this reference. This kind of reasoning is usually applied to the Universe as a whole, and this is also what Ned Wright seems to have had in mind. Your applying it to regions with different density within the Universe is innovative.

I thought of a "contraction of space" that affects only gravitationally bound systems, so that the Universe as a whole would not contract. This would be observationally equivalent to the familiar idea of an "expanding Universe". Extrapolating the calculations by F. I. Cooperstock et al., one would conclude that this "Hubble Lagrange point" must be very far out. It seems to me that the calculations by Cooperstock et al. are far from being realistic. If gravity between the galaxies within large clusters is still 107 times stronger than expansion, everything smaller than a Hubble sphere or so would be gravitationally bound. There could not be any voids smaller than this. Iggy, your comments suggest that you have a preconceived model in mind. Is there any more comprehensive description accessible?

Meanwhile, I have found relevant papers, such as Charlie Conroy et al. (2005) "The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics from z ~ 1 to z ~ 0" http://arxiv.org/PS_...8/0508250v2.pdf In the abstract, they say among other things that "We also clearly detect evolution in the VPF with cosmic time, with voids being larger in comoving units at z ∼ 0.", where VPF = "void probability function". Unfortunately, they do not show this in their paper in an easily verified and convincing way.

Since this is a more specific question than the one origianlly asked by URAIN, I started the new thread "Is the expansion of the Universe limited to voids?" where this is discussed. For a large list of different redshift mechanisms, see http://www.marmet.or.../mechanisms.pdf . The list includes also mechanisms that have not been proposed as explanations of the Hubble redshift, but of other phenomena.

Your claim was: This can only be a theoretical prediction. No such expansion has been observed. This is true, but it might be due to the smallness of the effects. So, my comment concerned the theoretical predictions. In the perhaps most popular model, it is assumed that the observed redshift in the spectra of distant galaxies are due to an "expansion of space". In this model, at least our instruments of measurement have to be excepted from this expansion. If everything up to superclusters of galaxies is excepted, your assertion is of course correct, but among researchers, there seems to be no consensus on where to draw the boundary.

This is correct if you adopt the "expanding Universe" view (Doppler shifts). As for the "expanding space" view, there is no consensus on this point. In this alternative, we and our measuring devices must be excepted from the expansion, and it depends on where the limit for this exception is placed.

Iggy, the first reference you gave us is to a FAQ by Ned Wright. Question: Are galaxies really moving away from us or is space just expanding? Answer: This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. ... This does not seem to be (or to have been) the majoity opinion, considering that the "expanding space" view dominates in text books, encyclopedias and popularizations, where the Doppler shift interpretation is often condemned. However, in the second reference you gave us (the third one was to the same paper by Bunn and Hogg "The kinematic origin of the cosmological redshift"), the expanding space view is condemned instead. This is an informative paper. I found the arguments in favour of the kinematic view convincing, but the arguments against the "expanding space" view less so. I also had a look at papers in which the Bunn & Hogg paper was quoted. Those who refer to it are mostly critical. The subsequent entry in the FAQ: Question: Why doesn't the Solar System expand if the whole Universe is expanding? Answer: This question is best answered in the coordinate system where the galaxies change their positions. ... This is a cheep way out, since the question becomes tricky only in the other coordinate system. Why don't the distances between the orbits of the planets increase with time if space expands? The same passage in the FAQ also contains a reference to Cooperstock et al. about which I mentioned earlier that they showed no awareness of the effects on their measuring devices. I also found a paper, "Expanding Space: the Root of all Evil?", http://arxiv.org/abs/0707.0380, in which it is attempted to put the "expanding space" view on a tenable foundation. Unfortunately, even in this paper, the question that bothers me is not touched. The authors behave like Ned Wright and Cooperstock et al. and so fail to notice the problem. I have not changed my opinion. The "expanding universe" view is not equivalent to the "expanding space" view. It is, on the contrary, equivalent to a "contracting space" view! "Expanding Universe": Galaxies move away from each other. Nothing special happens to light and to us and our devices. We see a Doppler shift. "Contracting space": Space contracts universally, including us and our devices. Nothing special happens to light. We see a redshift that looks like a Doppler shift. "Expanding space": Galaxies remain in place. Light waves are stretched on their way due to expansion of space. Although space expands, we and our devices do not expand. Where is the limit of this exception?

You are right. Universal expansion of space would not be observable if light that is on its way is affected in the same way as matter that is at rest (co-moving with the Hubble flow). If this is not the case, a frequency shift may be observable, but not necessarily a redshift. If it should be the case that light conserves its original features (since it moves along null geodesics and does not age), a blueshift will be observed. As long as light and matter are affected in the same way, I think it does not matter whether expansion is linear or not. I admit that it was a bit impressionistic. I think there is a difference between the two views in how the observer is affected, but I may change my opinion after having red the references. Thank you very much for these! In order to calculate the local density [math]\rho[/math], it is necessary to decide about the radius of the sphere, and this seems to involve an arbitrary decision. If you consider the gravitational potential [math]\Phi[/math], you do not have this problem (perhaps others). I have to read more carefully. The method you propose does work.

In the standard cosmology, the expansion is due to a Big Bang that just happened some time ago. "Dark Energy" is invoked in order to account for an apparent acceleration of this expansion.

When the Hubble redshift still was interpreted as a Doppler shift (galaxies rushing away from each other within a pre-existing space), there was nothing that would suggest any local expansion. Neither measurement devices nor galaxies were assumed to expand, and for galaxy clusters it came as a surprise that they do not contain enough mass to account for their cohesion. The Doppler interpretation was abandoned when the CMBR had been discovered. The FLRW-models predict a monopole anisotropy in this radiation. Such an anisotropy was not seen. Subsequently (I am not aware of any other reason), the expansion came to be attributed to space as such. This leads to the delimitation problem that bothers me, but which often goes unnoticed. If the problem is noticed, the limit is often drawn at the scale of galaxy clusters (gravitationally bound systems). There is no expansion at any smaller scale. However, this would be incompatible with the Big Bang paradigm at early times, when the size of the Universe was not yet large enough for housing any voids. Iggy mentioned the possibility of drawing the limit between regions below and above the critical density. This appears to me more reasonable, but the critical density does not have this function in the standard paradigm. It is also not immediately clear how a place-specific matter density should be defined. The "critical gravitational potential" is well-defined and could do the same job, but it also lacks this function in the standard paradigm. It has also been assumed that the expansion is universal, but in these cases, the effects on the measuring devices and standards have been overlooked. Truly universal expansion of space would not be observable. A redshift could be explained as due to a universal contraction of space, if it is assumed that light (moving along null-geodesics) is not affected, but I do not wish to argue for such a model.

Probalby you mean that the "rubber sheet" of the space-time fabric within gravity-bound objects is non-expanding. Then we agree, but this was just the preamble to the questions. There is a paper by Cooperstock, Faraoni and Vollick ”The influence of the cosmological expansion on local systems” (http://arxiv.org/PS_cache/astro-ph/pdf/9803/9803097v1.pdf). On p.4 they say: ”In this paper, we assume that homogeneous isotropic expansion is actually universal and we analyze the consequences of this assumption.” This means that they assume gravitational binding not to be the decisive factor. However, it seems to me that they do not actually live up to this assumption. They tacitly assume that at least the instruments of measurement (i.e., the standards of comparison) do not expand. If even these expanded, the expansion would not be observable.

In standard cosmology, the Hubble redshift in the light from distant galaxies is interpreted as due to an expansion of space. However, it is also said that within "gravitationally bound systems" up to the size of clusters and superclusters of galaxies, there is no such expansion. This means that the expansion occurs only within the voids between these. Now, I have two questions: First, how this is meant to be understood within the standard Big Bang cosmology. If we assume that only 0.1% of the volume of the Universe is filled with gravitationally bound systems, while the remaining 99.9% are voids, there was no space for voids when the age of the Universe was less than a tenth of what it is now. Thus, the rules must have been different then, in order to allow also gravitationally bound systems to expand. Second, are there any astronomical studies that have shown voids to expand (distant voids being smaller)? I would be grateful for explanations and for refernces to relevant papers.

In redshifted light, the wavelengths are longer, as if time was passing slower. This is called time dilation, and it has also been observed in the light curves of distant supernovae. Red shift increases with distance. Within the solar system, the effects are really very small, but in galaxies and galaxy clusters, they would be measurable.

We know that light from distant galaxies is redshifted and that this redshift increases approximately linearly with distance. This can be interpreted as due to a Doppler shift or an expansion of space, as in current doctrine – the Big Bang pardigm. Other explanations for the redshift have been proposed, but so far not found acceptance. We also know that within the solar system, within galaxies, within galaxy clusters and superclusters, there is no such expansion. Also on a lager scale, there are no indications of an overall expansion except for the redshift (time dialtion in ligtht). The Big Bang paradigm has to rely on a set of fudge factors such as dark matter, dark energy, size evolution of galaxies etc. in order to be brought into agreement with observations. Links: What is the currently most accepted model for the Universe? http://www.astro.ucla.edu/~wright/cosmology_faq.html#bestfit Angular size test on the expansion of the universe. http://arxiv.org/abs/1002.0525 A way out of the dark age in cosmology http://arxiv.org/abs/1107.2529 Is the Universe really expanding? http://arxiv.org/abs/1107.2485 Quantitative Comparison of Redshift Mechanisms http://www.marmet.org/cosmology/redshift/mechanisms.pdf