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There you have fallen into a trap for yourself. If the apparent acceleration of an object falling to an event horizon does not appear to slow down for an external observer then in the reference frame of the falling object it will achieve superluminal acceleration since distance over time has to take into account the stretching of spacetime, the resulting extended distance and the time dilation due to the increasing gravitational field strength.
So what distinction to you make between shell observers, freely falling observers and far-away observers? Why would you say the distinctions you make are important?
Luckily you and me don't have to solve this. It has already been solved. The Cartesian coordinate system that runs out at the Event horizon is replaced by the Eddington-Finkelstein coordinates. This coordinate system goes through (rs) to a singularity at the centre. Therefore the Event Horizon is represented by finite coordinates that are no different in essence to any other coordinates, outside that radius.
You do realise of course that the equations I posted take G=c=1 so that 2m IS the value for rs. Once I realised you didn't understand this I stopped reading.
Just in case anyone reading this gets confused, the Schwarzschild solution to the Einstein vacuum equation is the least likely one to occur in nature as the black hole it describes does not rotate. It is a useful model to work with as it is far simpler than models of rotating black holes such as the Kerr metric.
And all this even that far can only be considered for a non-rotating Black Hole.I don't believe such is actually possible.
I think that you Jeffrey, are basically agreeing with this view.Or have I misinterpreted the meaning of your posts?
I'm not agreeing with anything.