From: goldenfieldquaternions@gmail.com   
      
   On Monday, June 11, 2018 at 7:04:19 AM UTC-5, Gregor Scholten wrote:   
   > Sabbir Rahman wrote:   
   >   
   > >> A very informative diagram of the gravitational-collapse process can   
   > >> be found in figure 32.1c of Misner, Thorne, and Wheeler, "Gravitation"   
   > >> (W. H. Freeman, 1973).   
   > >> -- jt]]   
   > >   
   > > [Moderator's note:  There is a new edition of MTW out, at a reasonable   
   > > price to boot.  -P.H.]   
   > >   
   > > Please note that the discussion of spherical collapse in Ch.32 of MTW   
   > > does not address the issues I am raising here (if it did, there would   
   > > have been no point in my raising them as they would already have been   
   > > addressed!).   
   > >   
   > > Throughout that discussion in MTW, it is _assumed_ (without anywhere   
   > > making that assumption explicit presumably because it is taken to be   
   > > 'common sense') that the interior of the star and [the radial inward   
   > > progression of] the Schwarzschild interior refer to the same   
   > > (sub)manifold.   
   >   
   > I just read again the chapters 32.4 and 32.5 of MTW, and in fact, they   
   > write what I already explained: all the particles inside the collapsing   
   > dust cloud fall simultanously towards the point r = 0, there is no   
   > "encountering" of the outermost shell of particles and the more inner   
   > shells.   
   >   
   > In 32.4, they consider a dust cloud with zero pressure and argue that   
   > the metric inside the cloud equals the Friedmann metric of a contracting=   
      
   > universe. And like there is no encountering of shells of galaxies in a   
   > contracting universe, there is no encountering of shells of dust particle=   
   s.   
   >   
   > In 32.5, they consider a collapsing star with pressure gradient. They   
   > write that the surface of the star is no longer free-falling due to the   
   > forces caused by the pressure gradient, but that qualitatively seen the   
   > process of collaps is like in the case of zero pressure.   
   >   
   > So, I am really wondering what makes you think that the standard picture=   
      
   > would be that the outer shell of dust particles encounters the more   
   > inner shells and sweep them along with it?   
      
   I have not addressed this because I fear there is a bit of confusion.   
   The Oppenheimer-Snyder model is an idealism. It would pertain to a   
   huge collection of stars that fell from some outer location. Given   
   a billion stars mutually gravitating to a center. A billion solar   
   mass black hole has an horizon area of about 10^{19}km^2. A billion   
   stars could fall and fill this region without collisions, though   
   they would be getting close. However, before the black hole would   
   form with the horizon generated less than 1000th of volume would   
   be occupied by a star. This would be a model for how a black hole   
   could form in the Oppenheimer-Snyder model.   
      
   The question seems to be concerned with what happens in a real   
   collapse. This is a far more complex problem. The numerical relativists   
   have been working on this and related problems. Some are hard at   
   work looking at the gravitational wave signatures from the neutron   
   star collision to determine if that left a black hole. This and   
   related questions gets into matters of enormous complexity and   
   difficulty.   
      
   [[Mod. note -- The formation of a black hole by collapsing matter   
   is indeed a classic numerical-relativity problem.  May and White 1966   
   (Physical Review volume 141, page 141) was an early classic work.   
   Petrich, Shapiro, & Teukolsky 1985 (Physical Review D volume 31,   
   page 2459) is a more recent work.   
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
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