Reduced Hamiltonian for intersecting shells and Hawking radiation

TL;DR

This paper derives a reduced Hamiltonian for intersecting self-gravitating shells in a symmetric gravitational field and applies it to analyze semiclassical actions related to Hawking radiation.

Contribution

It introduces a new reduced Hamiltonian formulation for intersecting shells, including both massless and massive cases, and connects it to semiclassical Hawking radiation calculations.

Findings

Derived the reduced Hamiltonian for intersecting shells.

Applied the formulation to compute semiclassical actions.

Revisited the relation between action's imaginary part and Bogoliubov coefficients.

Abstract

We consider the dynamics of one or more self gravitating shells of matter in a centrally symmetric gravitational field in the Painleve' family of gauges. We give the reduced hamiltonian for two intersecting shells, both massless and massive. Such a formulation is applied to the computation of the semiclassical action of two intersecting shells. The relation of the imaginary part of the space-part of the action to the computation of the Bogoliubov coefficients is revisited.