From: intuitionist1@gmail.com   
      
   On Tuesday, June 12, 2018 at 1:22:43 AM UTC+3, Gregor Scholten wrote:   
   > Sabbir Rahman wrote:   
   >   
   > >>> At the   
   > >>> moment that the black hole forms at t=t0   
   > >>   
   > >> Where t is the time coordinate of some coordinate system in which the   
   > >> black hole forms within finite time, i.e. not Schwarzschild coordinate=   
   s,   
   > >> but e.g. Eddington-Finkelstein coordinates.   
   > >   
   > > The choice of coordinate system is not important   
   >   
   > It is important in that way that it must allow for indicating a time   
   > t=t0 when the black hole forms. This excludes e.g. Schwarzschild   
   > coordinates, in which t0 would be in the infinite future.   
   >   
   >   
   > >>> say, it is true that the   
   > >>> boundary conditions require that R(r=2M,t=t0)=S(r=2M,t=t0).   
   > >>   
   > >> You mean because at the surface of the collapsing celestial body, the   
   > >> metric R(r,t) must match the external Schwarzschild metric (outside th=   
   e   
   > >> body), and since this is known to match the internal Schwarzschild   
   > >> metric S(r,t) there, it must match internal Schwarzschild metric S(r,t),   
   > >> too?   
   > >   
   > > The metric outside the collapsing matter matches the exterior   
   > > Schwarzschild metric up until the formation of the black hole.   
   >   
   > You mean because you think that as soon as the radial coordinate R of   
   > the dust cloud's surface becomes < rs, the metric in the region R < r <   
   > rs would be the interior Schwarzschild metric? That's wrong. The metric   
   > in the region r > R is the exterior Schwarzschild metric everywhere,   
   > even after R has become < rs. So, in the region R < r < rs, the metric   
   > is the exterior Schwarzschild metric, like in the region r > rs.   
      
   I replied earlier to this, though the reply has yet to appear. Much   
   of the confusion that arose was due to our using different definitions   
   of "Schwarzschild interior metric". I was talking about the metric   
   associated with the vacuum Schwarzschild interior solution, NOT the   
   Schwarzschild interior metric that you provided a link to. It was   
   my mistake for not checking your link and realising that we were   
   talking about two completely different things.   
      
   In another message I have suggested a different ('rigid framework')   
   scenario which hopefully makes my topological splitting argument   
   clearer.   
      
   I not that you have also raised some further points here which I   
   will read and hopefully get back to you on.   
      
   Thanks,   
      
   Sabbir   
      
   [[Mod. note -- There is indeed confusion.  Perhaps you could be   
   clearer what you mean by the phrase "vacuum Schwarzschild interior"   
   solution?  I know of two solutions to the Einstein equations which   
   are commonly ascribed to Schwarzschild:   
   (a) the Schwarzschild black hole solution (which isn't "interior",   
       but rather extends out to r=infinity)   
   (b) the Schwarzschild star (which isn't vacuum, and whose matter   
       content isn't dust)   
   and neither of them really fit that phrase.   
   -- jt]]   
      
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