Reduced Hamiltonian for intersecting shells

TL;DR

This paper develops a generalized gauge for reduced Hamiltonian formulation in intersecting shells in general relativity, enabling analysis of their dynamics and tunneling probabilities without singularities.

Contribution

Introduces a new gauge suitable for intersecting shells, extending Hamiltonian treatment to multiple shells, including massive and massless cases.

Findings

Hamiltonian formulation for intersecting shells is established.

Emission probabilities of shells are independent, showing no correlation.

Method enables semiclassical tunneling probability calculations for multiple shells.

Abstract

The gauge usually adopted for extracting the reduced Hamiltonian of a thin spherical shell of matter in general relativity, becomes singular when dealing with two or more intersecting shells. We introduce here a more general class of gauges which is apt for dealing with intersecting shells. As an application we give the hamiltonian treatment of two intersecting shells, both massive and massless. Such a formulation is applied to the computation of the semiclassical tunneling probability of two shells. The probability for the emission of two shells is simply the product of the separate probabilities thus showing no correlation in the emission probabilities in this model.