From: intuitionist1@gmail.com   
      
   On Sunday, June 17, 2018 at 8:31:36 PM UTC+3, Gregor Scholten wrote:   
   > Sabbir Rahman wrote:   
   > > So, let us consider a generic spherically symmetric matter configuration   
   > > in which a black hole has just formed at radius R=2M, and without loss   
   > > of generality, let us assume that this is the smallest radius at which a   
   > > black hole forms in that configuration, so that *all* of the matter   
   > > inside R=2M is outside of its Schwarzschild radius, and can indeed be a   
   > > _long_ distance outside of its Schwarzschild radius, relatively speaking   
   > > at least for r strictly less than 2M.   
   >   
   > In other words: you consider the case that the radial coordinate R of   
   > the surface/boundary of the matter configuration currently matches the   
   > Schwarzschild radius rs = 2GM of that matter configuration, where M is   
   > the total mass of that configuration. So, the black hole has *not* just   
   > formed, it is rather currently *forming*.   
      
   I am not sure what you mean here. I started with the phrase "let us consider   
   a ... configuration in which a black hole has just formed..." - and you are   
   now stating that it has *not* just formed? Huh?   
      
   Just to clarify, the black hole has formed form the perspective of the   
   exterior r > 2GM, so that any matter falling inwards past r=2GM will   
   inevitably hit the singularity. That is the situation I am asking you to   
   consider. The interior matter at r<2GM remains oblivous to the formation of   
   the black hole at this point, even though it was responsible for its   
   formation.   
      
   Also, note that something cannot be 'forming' at an _instant_ in time,   
   because using the present continuous tense implies an action that is taking   
   place over a _period_ of time. I don't yet understand why you insist on   
   making this distinction. Let us see...   
      
   > More precisely, we have to   
   > distinguish two scenarios:   
   >   
   > (1) The matter configuration has always been as it is now, the radial   
   > coordinate R of the boundary has always been equal to 2GM, there has   
   > been no collaps before, no time when R was > 2GM. So, the black hole has   
   > never formed, and is not forming currently, but is on the edge between   
   > formed and not formed. Such a configuration would be highly unstable,   
   > though, there would a highly unstable equlibrium between gravity and   
   > repulsive forces - the slightest disturbance would destroy the   
   > equlibrium and cause gravity to become dominant so that the   
   > configuration would collaps. Therefore, such a scenario would be highly   
   > unrealistic.   
      
   I don't really understand your point, but clearly I have imposed no such   
   restriction on the configuration. Anyway, if the interior has mass M, and   
   the boundary is at R=2GM, then the black hole has already formed. At the   
   precise time of formation (i.e. at r<2GM), the matter in the interior is   
   oblivious to the formation of the black hole, and no matter how 'unstable'   
   or 'unrealistic' you consider the situation to be, the interior matter can   
   still in principle escape to infinity.   
      
   > (2) The matter configuration was collapsing before, so that R was > 2GM   
   > before. In the moment when the black hole is forming, i.e. R is exactly   
   > 2GM (as already emphasized, the black hole has *not* just formed in that   
   > moment, it *is* actually *forming*), gravity and repulsive forces could   
   > balance each other if we assume the repulsive forces are arbitrary   
   > strong, but the preceding collaps unavoidably makes up a disturbance to   
   > this balance, so that the repulsive forces are dominated by gravity and   
   > fail to support against further collaps. Even if we assume that the   
   > repulsive forces slow down the collaps when R is approaching 2GM from   
   > above, the collaps will always make up some at least slight disturbance,   
   > preventing an equlibrium to establish. So, in the moment when R equals   
   > 2GM, R is currently decreasing, even if the velocity of decreasing is   
   > very low. So, R unavoidably becomes < 2GM, and as soon as that happens,   
   > the black hole has formed, and a further collaps of the matter   
   > configuration cannot be avoided.   
      
   When R=2GM, the black hole has formed. The matter in the exterior will hit   
   the singularity if it crosses R=2GM. The matter in the interior (including   
   the outermost shell) is oblivious to the formation of the black, and can   
   still escape to infinity. For the interior, the repulsive forces can do   
   better than balance the gravitational force, it can exceed it, so that   
   again, the matter in the interior can in principle escape to infinity.   
      
   There is no problem with the interior collapsing further (i.e. to r<2GM) so   
   that more black holes are formed - however I have already explained that   
   the situation can get a bit complicated in this case, forming a frozen star   
   in the case of a collapsing dust cloud. At no point can the mass inside   
   radius r be greater than r/2G. Any additional mass that crosses that radius   
   r will be diverted to the Schwarzschild singularity associated with the   
   black hole formed at that radius.   
      
   > > Let us ignore the matter outside of R=2M for now (we could suppose for   
   > > convenience that there is none, without changing the basic argument),   
   > > and let us focus on the infinitesimal shell of matter that has just   
   > > caused the black hole to form.   
   >   
   > It has not caused the black to form, it currently is causing the black   
   > hole to form.   
      
   No it has actually caused the black hole to form. See above. This   
   infinitesimal shell is not aware however that the black hole has formed, and   
   it does not end up in the associated singularity. It _might_ however end up   
   falling in to the singularity of a different black hole that forms in the   
   interior following further collapse.   
      
   > > I think before in this thread I may have been a bit sloppy and said (or   
   > > at least implied) that this infinitesimal shell of matter is inside its   
   > > Schwarzschild radius when the black hole forms.   
   > >   
   > > In actual fact, if we are more careful, we will realise that _none_ of   
   > > that infinitesimal shell lies inside its Schwarzschild radius. Indeed   
   > > only particles _outside_ that shell feel the effect of the full mass M.   
   > > That infinitesimal shell itself only feels the effect of the mass M-dm,   
   > > where dm is the infinitesimal mass of that shell.   
   >   
   > And because of this, the black hole has actually not yet formed (it   
   > rather is currently forming), and the gravitational forces on that shell   
   > can just be balanced by repulsive forces. But due to the preceding   
   > collaps, that made the radial coordinate R of the shell decrease from >   
   > 2GM to 2GM, there is some at least slight disturbance that destroys the   
   > balance, so that the gravitational forces dominate the repulsive forces   
   > and the collaps continues.   
      
   Okay, let me try to clarify this again for you. You are correct in that no   
   black hole has formed from the perspective of the infinitesimal mass shell   
      
   [continued in next message]   
      
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