From: helbig@asclothestro.multivax.de   
      
   In article , Steven Carlip   
    writes:   
      
   > On 5/1/19 2:25 AM, p.kinsler@ic.ac.uk wrote:   
   >> Steven Carlip  wrote:   
   >>> Finally, as a slightly more subtle point, the two elements of general   
   >>> relativity I listed aren't really independent.  It turns out that the   
   >>> Einstein field equations -- the equations that determine the curvature   
   >>> of spacetime in terms of its matter content -- are all you need.  If   
   >>> you try to write down a solution of the field equations with two   
   >>> separate lumps of matter, you find that there is no solution for which   
   >>> the lumps are stationary.  Solutions *only* exist if each piece is   
   >>> already moving properly in the other's gravitational field.   
   >   
   >> Just a request for clarification - are you saying it can be proven   
   >> that no such "both stationary" solutions can exist?   
   >   
   > Yes.   
      
   As Steve notes, there is no static solution for "two lumps".  However,   
   there is a static solution, namely the first relativistic cosmological   
   model, developed by Einstein.  Here, a finite but unbounded universe has   
   the same density everywhere.  However, static solutions exist only if   
   there is a cosmological constant (a necessary but not sufficient   
   condition).  In fact, Einstein first found no static solution, but he   
   expected one since, at the time, the general wisdom was that there are   
   no large-scale motions in the universe, so he modified his equations to   
   include the cosmological constant.   
      
   It is important to realize that this is not a "fudge factor".  One could   
   have formulated GR with the cosmological constant from the beginning,   
   leaving it as a free parameter the magnitude of which is determined by   
   observation (just like the gravitational constant).  That this didn't   
   happen is more an accident of history.  Alien intelligences will find   
   the same GR, but probably via a very different route.   
      
   Although the only source is the somewhat untrustworthy George Gamow, and   
   some scholars dispute his report, legend has it that Einstein called   
   this his "biggest blunder".  Whether or not he said that or words to   
   that effect, this has no bearing on whether the cosmological constant   
   exists or not, though some would think so ("Even Einstein said...").   
   Einstein was often wrong.  (For a while, he didn't believe in the   
   reality of gravitational waves.  His mistrust of quantum theory is   
   probably unfounded.  And so on.)   
      
   On the other hand, had he left it out, he could have predicted that the   
   universe is expanding (or contracting---this depends only on initial   
   conditions; in particular, the cosmological constant is not the cause of   
   the expansion of the universe, though it is the cause of the   
   acceleration).   
      
   Einstein later favoured a closed universe without a cosmological   
   constant (in such a case, spatially closed (finite) implies temporarily   
   closed (big crunch in the future); in general this is not the case), and   
   also suggested a spatially flat universe with no cosmological constant,   
   together with de Sitter.  Their motivation was that this is a simple   
   model, and at the time observations weren't good enough to rule it out,   
   so they suggested it for reasons of "logical economy".  It later became   
   the "standard model" among people who believe both that inflation   
   predicts a (nearly) flat universe and that there is no cosmological   
   constant.  That has since been ruled out by observations, and the   
   current standard model is (nearly) flat but has an appreciable   
   cosmological constant (the corresponding energy density is more than   
   twice that of matter (including the mysterious dark matter).   
      
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