From: intuitionist1@gmail.com   
      
   On Wednesday, June 13, 2018 at 2:09:42 AM UTC+3, Gregor Scholten wrote:   
   > Sabbir Rahman wrote:   
   > > Not really. I am using this special case to try to make it easier for   
   > > you to understand the general case. I have read quite a few sources on   
   > > the subject of gravitational collapse. They all force the matter in the   
   > > interior of the black hole to be crushed into a singularity as the   
   > > Schwarzschild exterior collapses towards it. The matching of boundary   
   > > conditions to the Schwarzschild exterior is essentially what forces the   
   > > 'sweeping' to take place. Amongst other things, I am arguing that this   
   > > boundary condition is incorrect because there is no longer a physical   
   > > link between the matter interior and the Schwarzschild exterior after   
   > > the black hole has formed.   
   >   
   > And this argument is wrong. As we have seen, the metric for r > R is   
   >   
   > S_M(r,t)   
   >   
   > where R is the radial coordinate of the boundary (surface) of the matter   
   > distribution ("rigid" structure + dust shells in your case) and S_M is   
   > the Schwarzschild metric for the mass M = M(R,t). No matter if R < 2GM   
   > or R > 2GM. For r < R, the metric is   
   >   
   > R(r,t) = S_{M(r,t)}(r,t)   
   >   
   > with S_{M(r,t)} being the Schwarzschild metric for the mass M(r,t) <= M   
   > that is contained in r.   
   >   
   > If a shell of the matter discribution that is at r + dr at time t   
   > encounters a more inner shell at r at time t + dt, then the matter   
   > distribution is at r changed from M(r,t) to M(r,t+dt), changing the   
   > metric at r from   
   >   
   > R(r,t) = S_{M(r,t)}(r,t)   
   >   
   > to   
   >   
   > R(r,t+dt) = S_{M(r,d+dt)}(r,t+dt)   
   >   
   > Where we have to note that after the formation of a black hole, and   
   > already a little earlier, that case cannot occur that a shell is static   
   > (like the rigid structure in your scenario).   
   >   
   > At every r and t (apart from the singularity), the metric is smooth (no   
   > abrupt change between r and r + dr or t and t + dt), so there is a   
   > physical link everywhere.   
      
   Okay, here is the problem I have with this. Any infalling matter outside   
   the dust cloud experiences the full mass M of the interior, and thus on   
   crossing the event horizon is doomed to hit the singularity after some   
   period of time that depends upon M.   
      
   Your analysis above for the matter in the interior is fine and I have no   
   issues with it. HOWEVER, there is a priori no singularity there, and   
   neither does there necessarily ever have to be.   
      
   Thus, we _do_ have two incompatible metrics here - the Schwarzschild black   
   hole metric for a black hole of mass M, and the metric R(r,t) that you   
   have described above, which is indeed Schwarzschild, but always for some   
   mass M(R) < M for r < 2GM.   
      
   As I have already said, for these two metrics to coexist, a topological   
   bifurcation must occur when the black hole forms.   
      
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