From: g.scholten@gmx.de   
      
   Sabbir Rahman wrote:   
      
   > 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   
      
   In fact, the latter is not true, though. As I realized in the meantime,   
   your main argument that the outermost shell would experience the gravity   
   of the mass M - dm only, instead of the full mass M, is wrong. The   
   reason is that every shell is self-attractive. Imagine a shell of   
   thickness dr as composed of elements of volume   
      
   d^3r = (g_rr)^(1/2) r sin(theta) dr dtheta dphi   
      
   each. Then these elements attract each other, making the shell as a   
   whole attract itself. A shell of mass dm on its own would therefore   
   experience the gravitational attraction of the mass dm, and as the   
   outermost shell of a spherically symmetric matter configuration of mass   
   M, it experiences the gravitational attraction of the full mass M, not   
   of the mass M - dm of the more inner shells only.   
      
   A shell at a radial coordinate r does not experience any gravitational   
   forces from more outer shells, that is correct, but experiences   
   gravitational forces from itself.   
      
   So, no matter if the radial coordinate R of the outermost shell is at   
   2GM or at 2GM - dr, in both cases the outermost shell is not able to   
   resist against gravity, since it experiences the gravity of the full   
   mass M, and therefore is unavoidably forced to fall inwards. In the same   
   manner as an infalling particle that crosses the radial coordinate R.   
      
   So both, the outermost shell and the infalling particle experience the   
   same metric.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)