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: 

¹<http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap12.pdf> Page 4 chapter 1.2  

²<http://www.roma1.infn.it/teongrav/leonardo/bh/bhcap3.pdf>
Page 50 chapter 3.4.2