Hamiltonian treatment of Collapsing Thin Shells in Lanczos-Lovelock's theories

TL;DR

This paper develops a Hamiltonian framework to analyze the collapse of thin shells in Lanczos-Lovelock theories, showing black hole formation is possible while naked singularities are generally avoided, except in Chern-Simons cases.

Contribution

It introduces a Hamiltonian formalism for thin shell collapse in Lanczos-Lovelock theories, highlighting the unique behavior of Chern-Simons gravity regarding naked singularities.

Findings

Black holes can form via thin shell collapse in most Lanczos-Lovelock theories.

Naked singularities are generally not formed, except in Chern-Simons theory.

Chern-Simons theory lacks a Newtonian-like gravitational self-interaction.

Abstract

The Hamiltonian treatment for the collapse of thin shells for a family of Lanczos-Lovelock theories is studied. This formalism allows us to carry out a concise analysis of these theories. It is found that the black holes solution can be created by collapsing a thin shell. Naked singularities cannot be formed by this mechanism. Among the different Lanczos-Lovelock's theories, the Chern-Simons' theory corresponds to an exceptional case, because naked singularities can emerge from the collapse of a thin shell. This kind of theory does not possess a gravitational self-interaction analogous to the Newtonian case.