Why one cannot escape from a black hole The usual explanation is that escape velocity of a black hole is above speed of light, therefore nothing can escape because nothing can move faster than light.

This is however a fallacy, because escape velocity only pertains to bodies "without propulsion", or in other words without any force other than gravity acting on them. As an example I could theoretically escape Earth's gravity at a walking speed, just give me a staircase and I could walk all the way to the Moon. No need to accelerate to 11 km/s at any point.

How does this affect black holes? Why cannot I have a staircase and climb out?

I know the staircase idea must be wrong, but I would like to know why. My guess is that I am applying Newtonian mechanics to a problem which requires general relativity approach, because Newtonian mechanics approximation fails badly around such massive gravity fields?

Anyway, according to Newtonian mechanics one can easily escape a black hole, even if we assume that speed of light cannot be exceeded.
A great explanation; all credit goes to: https://groups.google.com/forum/#!original/sci.physics.research/PZh0yawL2nA/YKbv-EpWJPsJ


  The explaination of a black hole in terms of escape velocity is not a
  good way to think of a black hole. The escape velocity is merely the
  intial speed at which a projectile must be fired from a large body in
  order so that, given that only gravitational forces act on it (which
  is a scenario very far from reality) it will never return to that
  body.
  
  However, anything that passes through the event horizon of a black
  hole will never be on the other side. Even if it were to constantly
  accelerate away from the black hole, it would still be going inward.
  This is not true of Newtonian gravity. In fact, in Newtonian gravity,
  there are no black holes, because there is no universal speed limit.
  
  The best way to think of an event horizon is where spacetime is so
  bent that all paths 'curve inwards', IE, the lightcones all point
  inward, so there is no chance of escape.
  
  BTW, in GR, it's not good to explain the effects of gravity as a
  FORCE. It is as much a force as the Centrifugal Force or the Coriolis
  Force. There is an amount of force needed to stay the same distance
  from an object, IE, to overcome gravity, however. And as you approach
  the black hole, the amount of force required approaches infinity. But
  to say that there is an infinite amount of force PULLING on someone is
  not very accurate.