The boundary conditions at infinity

  • #36
Ken G said:
Why wasn't de Sitter's model dynamic?
De Sitter's model was considered stationary (not static) because, as it didn't contain matter, it presented the same appearance at all times.
 
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  • #37
With "static" I mean there are spacetime coordinates so that all ##g_{\mu \nu}## do not depend on the time-like coordinate.
 
  • #38
vanhees71 said:
you can transform it to "static coordinates"
Yes, but those only cover a portion of the spacetime. De Sitter's original coordinates cover the entire spacetime (and AFAIK are the only ones that do of the commonly known coordinate charts on de Sitter spacetime). The entire spacetime is not static; but the region covered by the static coordinates is.

It's worth noting here that de Sitter spacetime has a ten parameter group of Killing vector fields, just as Minkowski spacetime does. The KVF that is timelike in the static region corresponds to the Rindler KVF in Minkowski spacetime.
 
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  • #39
Jaime Rudas said:
De Sitter's model was considered stationary (not static)
No, it is static, or at least the static region is. "Stationary" means that there is a timelike KVF; "static" means that the timelike KVF is hypersurface orthogonal. The latter condition is met in de Sitter spacetime in the static region.
 
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  • #40
Ken G said:
Yes, we tend to leave that out in the story of Hubble. Even Hubble did not immediately accept his observations as compelling evidence of an expanding time dependent universe
In fact, it seems that Hubble always had doubts about expansion and/or did not fully understand its physical nature, as can be seen in the quotes from the following papers:

A Clue to the Structure of the Universe (1929):

Here is a distance-velocity relation which probably holds out as far as the observations reach. It is difficult to believe that the velocities are real; that all matter is actually scattering away from our region of space. It is easier to suppose that the light-waves are lengthened and the lines of the spectra are shifted to the red, as though the objects were receding, by some property of space or by forces acting on the light during its long journey to the Earth.

The problem is now in the hands of the theorists [...]
https://articles.adsabs.harvard.edu/pdf/1929ASPL....1...93H

The Velocity-Distance Relation among Extra-Galactic Nebulae (1931):

The constancy of Mn is believed to be well established, hence apparent magnitudes of nebulae are accepted as measures of distance. The interpretation of red-shifts as actual velocities, however, does not command the same confidence, and the term “velocity” will be used for the present in the sense of “apparent” velocity, without prejudice as to its ultimate significance.
https://articles.adsabs.harvard.edu/pdf/1931ApJ....74...43H

The Observational Approach to Cosmology (1937):

We may state with some confidence that red-shifts are the familiar velocity-shifts, or else they represent some unrecognized principle of nature. We cannot assume that our knowledge of physical principles is yet complete; nevertheless, we should not replace a known, familiar principle by an ad hoc explanation unless we are forced to that step by actual observations.
[...]
The situation can be described as follows. Red-shifts are produced either in the nebulae, where the light originates, or in the intervening space through which the light travels. If the source is in the nebulae, then red-shifts are probably velocity-shifts and the nebulae are receding. If the source lies in the intervening space, the explanation of red-shifts is unknown but the nebulae are sensibly stationary.
https://ned.ipac.caltech.edu/level5/Sept04/Hubble/paper.pdf

The Problem of the Expanding Universe (1942):

The red shifts are frequently explained as velocity shifts (Doppler shifts), indicating actual recession of the nebulae at the rate of about 100 miles per second for each million light years of distance. The phenomenon has been observed out to about 240 million light years where the apparent velocities are nearly 25,000 miles per second. It may be stated with confidence that red shifts either are velocity shifts or they must be referred to some hitherto unrecognized principle in nature.
https://www.science.org/doi/10.1126/science.95.2461.212

From the above, it seems to me that Hubble wasn't clear that one thing doesn't exclude the other, because galaxies do indeed recede and the redshift is a product of what happens to light "during its long journey to Earth", that is, the expansion of space.
 
  • #41
It's interesting that Hubble says "the problem is now in the hands of the theorist" in 1928, when the theorists had already published solutions to the problem six years before.
 
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  • #42
PeterDonis said:
It's interesting that Hubble says "the problem is now in the hands of the theorist" in 1928, when the theorists had already published solutions to the problem six years before.
Well, but we must bear in mind that this was published in July 1929, that is, when, apparently, the only one who had paid attention to the works of Friedmann and Lemaître was Einstein.
 
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