Dynamics of a self gravitating light-like matter shell with spherical symmetry

TL;DR

This paper develops a Hamiltonian framework for a spherically symmetric, light-like, self-gravitating shell, providing explicit formulas and geometric insights, potentially serving as a simplified model for quantum gravity.

Contribution

It introduces a novel Hamiltonian description of light-like matter shells in spherical symmetry, with explicit gauge-invariant formulations and geometric interpretations, advancing canonical gravity models.

Findings

Explicit Hamiltonian in terms of true degrees of freedom

Geometric interpretation of conjugate momentum

Models of matter compatible with shell dynamics

Abstract

A novel Hamiltonian description of the dynamics of a spherically symmetric, light-like, self-gravitating shell is presented. It is obtained via the systematic reduction of the phase space with respect to the Gauss-Codazzi constraints, model and rare procedure in the Canonical Gravity. The Hamiltonian of the system (numerically equal to the value of the ADM mass) is explicitly calculated in terms of the gauge-invariant "true degrees of freedom", i.e. as a function on the reduced phase space. A geometric interpretation of the momentum canonically conjugate to the shell's radius is given. Models of matter compatible with the shell dynamics are found. A transformation between the different time parameterizations of the shell is calculated. The presented model may become a new toy model of quantum gravity.