Phantom shell around black hole and global geometry

TL;DR

This paper analyzes the dynamics of a thin phantom shell around a Schwarzschild black hole, classifying possible evolutions and showing that phantom energy flow remains undetectable to observers, with implications for astrophysics.

Contribution

It provides a comprehensive classification of the evolution scenarios of phantom shells around black holes, including cases with positive and negative shell mass, and explores their global spacetime structures.

Findings

Three evolution scenarios for positive shell mass with infinite motion and collapse.

Classification of analogous scenarios for negative shell mass.

Phantom energy flow remains undetectable by physical observers.

Abstract

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 equation of state are derived and analyzed. The different types of space-time 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 the physical observer to detect the fantom energy flow. We shortly discuss the importance of our results for astrophysical applications.