Minisuperspace, WKB, Quantum States of General Relativistic Extended Objects

TL;DR

This paper develops a method to derive WKB quantum states for relativistic thin shells in general relativity, utilizing an effective Lagrangian approach and Israel junction conditions, with an illustrative example.

Contribution

It introduces a general procedure to obtain WKB states for gravitating shells using an effective Lagrangian and junction conditions, advancing quantum modeling of such systems.

Findings

Established a method to derive WKB states for shells

Applied the approach to a specific example

Enhanced understanding of quantum states in gravitating systems

Abstract

The dynamics of relativistic thin shells is a recurrent topic in the literature about the classical theory of gravitating systems and the still ongoing attempts to obtain a coherent description of their quantum behavior. Certainly, a good reason to make this system a preferred one for many models is the clear, synthetic description given by Israel junction conditions. Using some results from an effective Lagrangian approach to the dynamics of spherically symmetric shells, we show a general way to obtain WKB states for the system; a simple example is also analyzed.