The phantom shell around a black hole and global geometry

We describe the possible scenarios for the evolution of a thin spherically symmetric self-gravitating phantom shell around the Schwarzschild black hole. The general equations describing the motion of the shell with a general form of the equation of state are derived and analysed. The different types of spacetime R± and T± regions and shell motion are classified depending on the parameters of the problem. It is shown that in the case of a positive shell mass there exist three scenarios for the shell evolution with an infinite motion and two distinctive types of collapse. Analogous scenarios were classified for the case of a negative shell mass. In particular, this classification shows that it is impossible for a physical observer to detect the phantom energy flow. We shortly discuss the importance of our results for astrophysical applications