From: intuitionist1@gmail.com   
      
   On Tuesday, June 12, 2018 at 11:52:01 AM UTC+3, Sabbir Rahman wrote:   
   > 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]]   
      
   I am referring to the Schwarzschild black hole solution. By the   
   "Schwarzschild interior" I mean the region inside the Schwarzschild   
   surface (which is at r=2M in Schwarzschild coordinates) that contains   
   the singularity. By "Schwarzschild exterior" I mean the region outside   
   the Schwarzschild surface that extends to infinity. Obviously this is a   
   vacuum solution, and hence the "vacuum" qualifier to try to distinguish   
   it from your and Gregor's non-vacuum "Scwarzschild interior".   
      
   I _think_ that you and Gregor are using "Schwarzschild exterior" to   
   refer to the entire Schwarzschild black hole solution, with the   
   'exterior' qualifier referring to the fact that this is the metric   
   exterior to the dust cloud.   
      
   If you have preferred names for the two regions in the Schwarzschild   
   black hole solution that I am referring to (i.e. inside and outside the   
   Schwarzschild surface) then please let me know so that we can try to   
   avoid this kind of confusion going forward. In the meantime I will refer   
   to them as the Schwarzschild black hole interior and exterior   
   respectively.   
      
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