# Collapse and Expansion of Scalar Thin-Shell for a Class of Black Holes

## TL;DR

This paper studies the dynamics of scalar thin-shells around various black holes, revealing how charge and rotation influence collapse and expansion behaviors, with implications for black hole physics.

## Contribution

It formulates equations of motion for scalar thin-shells around Schwarzschild, Kerr, and Kerr-Newman black holes using Israel formalism and provides numerical analysis of their collapse and expansion.

## Key findings

- Massive scalar shells lead to collapse.
- Massless scalar shells can collapse or expand.
- Charge and rotation affect shell dynamics.

## Abstract

This paper investigates the dynamics of thin-shell in the presence of perfect fluid as well as the scalar field. We formulate the equations of motion using Israel thin-shell formalism by taking the interior and exterior regions of Schwarzschild, Kerr as well as Kerr-Newmann black hole. We find numerical solutions of equations of motion and effective potential to analyze the scalar shell for collapse and expansion. It is found that the rate of collapse and expansion of scalar shell through shell's radius depends on charge and rotation parameters. We conclude that the massive scalar shell leads to a collapse of thin-shell, while massless scalar shell indicates both collapses as well as expansion.