How do we know we cannot escape the event horizon? A doubt assails me: deepening the Schwarzschild and Kerr space-times I found a beautiful article of the University of Rome, which provides a method to identify an event horizon based on the analysis of the square norm of constant "radial" coordinate hypersurfaces normal vector ¹ ².
In particular, taking advantage of the Strong Equivalence Principle, it is easily demonstrated that if the normal vectors are timelike the tangent vectors are spacelike i.e. once we enter the horizon we can no longer go out.
The question is: since gravity is a geometric property of space-time, how can we be sure that by heavily disturbing the region of the event horizon this effect is not destroyed i.e. it is possible to escape from the horizon itself?
Let me explain better: by introducing any energy source, gravity changes i.e. space-time changes. Considering that the horizon manifests itself through a geometric property (gravity), how can we be sure that the prediction "is impossible to get out of an event horizon" is valid even if on the horizon there is a star, an asteroid or, in general, an object with non-negligible energy effects capable of significantly altering the geometry of space-time?
Sources: 
¹http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap12.pdf Page 4 chapter 1.2
²http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap3.pdf
Page 50 chapter 3.4.2
 A: I can't give you an authoritative answer, but in the absence of one I'll attempt to at least clarify the problem.
The situation you describe is complex because there are no known analytic solutions for the two body system in GR. So there is no simple way of describing the modification of the Schwarzschild or Kerr geometry caused by your test mass. The test mass will certainly perturb the horizon but not in a way that is easy to calculate.
For large masses this is the merging black hole problem and numerical techniques for calculating the geometry are now routine courtesy of all the work done in support of the LIGO experiment. The horizon evolves in the way you'd intuitively expect i.e. it evolves from two separate Kerr geometries through to a final Kerr geometry passing through various shapes on the way.
What would be more interesting is if there was a way of analytically approximating the perturbation in the limit of a small but not negligible test mass. However I have never seen a calculation of this type.
A: The second law of black hole thermodynamics can be proved in GR, and it says that the area of the event horizon always increases. So you cannot eliminate the event horizon by introducing the gravitational field of some second object. Furthermore, area can't be transferred from one black hole to another, and black holes can't bifurcate (Hawking and Ellis, prop. 9.2.5, pp. 315-316). Intuitively, what this is telling us is sort of that once a black hole grabs a particular region of space, it will never relinquish any of it.
