acceleration of static observer near black hole horizon I am studying a paper which states, that the interaction of BH with external object, a BH can not be isolated.. but here in the given link an isolated BH is considered.. an anyone could explain this or share the article "http://inspirehep.net/record/10066" 
 A: The well known black hole metrics like the Schwarzschild and Kerr metrics describe black holes that are completely isolated. That is, the black hole is the only object in the whole universe. Obviously this is not true to any real black hole that we might observe in our universe. However as long as there aren't any large masses near the black hole we expect the Schwarzschild and Kerr metric to be excellent approximations.
The other approximation commonly used is that the observer does not affect the black hole. That is the mass of the observer/test object is so small that its gravity can be neglected. Since the black hole mass is many orders of magnitude bigger than the mass of a human, or even a spaceship, this is also an excellent approximation.
The paper you link calculates the proper acceleration assuming the black hole is isolated and that the mass of the observer can be neglected, and unless there are very unusual circumstances, e.g. the black hole is a close binary, it will be a very good approximation to the real proper acceleration. In fact it will be such a good approximation that for all intents and purposes we can consider it an exact calculation.
