[HN Gopher] Godel's Solution to Einstein's Field Equations
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       Godel's Solution to Einstein's Field Equations
        
       Author : privatdozent
       Score  : 14 points
       Date   : 2021-07-27 08:22 UTC (2 days ago)
        
 (HTM) web link (www.privatdozent.co)
 (TXT) w3m dump (www.privatdozent.co)
        
       | fxj wrote:
       | https://en.wikipedia.org/wiki/G%C3%B6del_metric
       | 
       | This solution has many unusual properties--in particular, the
       | existence of closed timelike curves that would allow time travel
       | in a universe described by the solution. Its definition is
       | somewhat artificial in that the value of the cosmological
       | constant must be carefully chosen to match the density of the
       | dust grains, but this spacetime is an important pedagogical
       | example.
       | 
       | The solution was found in 1949 by Kurt Godel.
       | 
       | The Godel metric is an exact solution of the Einstein field
       | equations in which the stress-energy tensor contains two terms,
       | the first representing the matter density of a homogeneous
       | distribution of swirling dust particles (dust solution), and the
       | second associated with a nonzero cosmological constant (see
       | lambdavacuum solution). It is also known as the Godel solution or
       | Godel universe.
       | 
       | Following Godel, we can interpret the dust particles as galaxies,
       | so that the Godel solution becomes a cosmological model of a
       | rotating universe. Besides rotating, this model exhibits no
       | Hubble expansion, so it is not a realistic model of the universe
       | in which we live, but can be taken as illustrating an alternative
       | universe, which would in principle be allowed by general
       | relativity (if one admits the legitimacy of a nonzero
       | cosmological constant). Less well known solutions of Godel's
       | exhibit both rotation and Hubble expansion and have other
       | qualities of his first model, but travelling into the past is not
       | possible. According to S. W. Hawking, these models could well be
       | a reasonable description of the universe that we observe, however
       | observational data are compatible only with a very low rate of
       | rotation.[4] The quality of these observations improved
       | continually up until Godel's death, and he would always ask "is
       | the universe rotating yet?" and be told "no, it isn't".[5]
       | 
       | Many other exact solutions that can be interpreted as
       | cosmological models of rotating universes are known. See the book
       | Homogeneous Relativistic Cosmologies (1975) by Ryan and Shepley
       | for some of these generalizations.
        
       | oh_sigh wrote:
       | This article might have better discussion around it if you could
       | read beyond the first sentence.
        
       | art_kimides wrote:
       | anyone have a password they can share?
        
         | art_kimides wrote:
         | On second thought, since the author is taking advantage of HN
         | to advertise their product, perhaps they should consider making
         | more of the essay available so that potential customers can
         | ascertain they aren't purchasing click bait or some inane
         | twiddle twaddle.
        
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