Can mass be ejected from a black hole within the Schwarzschild radius? This goes far beyond my limited knowledge regarding the physics of black holes, but my colleague told me this today: 

I doubt that if I stand on the surface of a black hole - inside the
  Schwarzschild radius - and a stone falls on my head from outside the
  Schwarzschild radius, it cannot come out again. Then I just have to
  throw it back up with the energy it fell on my head so that it leaves
  the black hole. The stone can accept this energy because he fell on my
  head with it. Otherwise, the physical laws of gravity no longer apply.
  Just try to let a stone vibrate in a gravitational field whose
  generating mass has no expansion and idealizes does not collide with
  the vibrating body. It does not get stuck in the point x=0, but flies
  out again with infinite energy against an infinite acceleration. And
  this in clearly finite time.
If you have managed this calculation, then the question arises, where
  the energy should go, if the stone can fall in, but not fall out
  again? Energy is simply the time integral of the acceleration equation
  after multiplying both sides by the corresponding velocity equation.
  Since due to the existence of the acceleration equation also the
  velocity equation exists, the energy a body has in a force field is
  fixed for every movement. And this energy is on the way there, the
  same as on the way back, because it depends only on the place and not
  on the time. Even if time is deformed and the path is compressed,
  energy and place remain firmly connected. So the stone comes out of
  the black hole.

I wanted to share this with the community in order to get a clearer perspective to his statement. Are his assumptions correct? If so is there proof and maybe further literature? 
(As far as I remember, the jets coming from super massive black holes do not contain anything from beyond the Schwarzschild radius.)
 A: This exceprt doesn't quite get what a black hole is.  Once you're inside the Schwarzschild radius, it's not that "you can't go fast enough too get out", it's that the idea of "going outside of the black hole" is a concept that doesn't make sense.  Once you are inside, all timelike paths (which are the allowable physical paths of objects that move from the past into the future) end in the black hole singularity.  
A: I don't know what surface of black hole means, but you cannot stand on the fixed radius from centre of gravitational field (center of black hole) without having superluminal speed. 
The problem is that inside event horison the spacetime becomes dynamic - you can imagine space itself is collapsing and it is collapsing quickly enaugh to prevent anything that does not have superluminal speed from escaping. Yes you can throw the object away from the center, but because the space itself collapses to the center the net effect is that the object will always move to the center no matter how much energy you provide
The next problem is that there is no energy conservation in GR in the sense it is in newtonian mechanics. The energy is conserved only locally, not globally. The energy is not even defined globally - simply because due to equivalence principle you cannot define energy of gravitational field itself. In local inertial frame there is no gravitational field. The supposed energy accumulated by falling in gravitational field is not due to the fall of object, it is due to the acceleration needed to remain still in gravitational field.
The energy of an object is simply projection of objects 4-velocity onto your own 4-velocity. The objects 4-velocity remains "the same" (is parallel transported) during the fall, but your own is accelerated and thus is changing in any local inertial frame around you. The percieved kinetic energy of the object is not increasing in the free fall due to objects motion, but due to your own acceleration. Sometimes this can be mathematically reformulated so that you can associate changes of kinetic energy with freely falling object itself like in newtonian limit, but not in general.
This is all very sloppy of course, because i assume you don't know much about mathematic that is needed to formulate the ideas precisely. If you want to learn it though, i would recommend Gravitation by Misner, Wheeler and Thorne. Its huge book, but you don't need to read everything and all the ideas are explained very inuitively as well as mathematically
