Hamiltonian Treatment of the Gravitational Collapse of Thin Shells

TL;DR

This paper develops a Hamiltonian framework for analyzing the gravitational collapse of thin shells, reproducing known dynamics and extending to charged and rotating black holes in three dimensions, demonstrating their stability against collapse into naked singularities.

Contribution

It introduces a Hamiltonian formalism for thin shell collapse, including charged and rotating cases in 3D, and shows black hole stability against shell-induced naked singularities.

Findings

Reproduces standard shell dynamics via canonical constraints

Extends formalism to charged and rotating black holes in 3D

Shows black holes cannot become naked singularities through shell collapse

Abstract

A Hamiltonian treatment of the gravitational collapse of thin shells is presented. The direct integration of the canonical constraints reproduces the standard shell dynamics for a number of known cases. The formalism is applied in detail to three dimensional spacetime and the properties of the (2+1)-dimensional charged black hole collapse are further elucidated. The procedure is also extended to deal with rotating solutions in three dimensions. The general form of the equations providing the shell dynamics implies the stability of black holes, as they cannot be converted into naked singularities by any shell collapse process.