The wave function of a gravitating shell

TL;DR

This paper derives an exact analytical quantum wave function for a thin gravitating shell in Reissner-Nordstrom spacetime, revealing the absence of an extreme state in its spectrum, contrasting with extreme black holes.

Contribution

It provides a new exact solution for the quantum wave function of a gravitating shell using Meixner polynomials, advancing understanding of quantum black hole models.

Findings

Discrete spectrum calculated for the gravitating shell

Exact analytical solution in terms of Meixner polynomials

No extreme state found in the quantum spectrum

Abstract

We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wave function of a thin gravitating shell in the Reissner-Nordstrom geometry. We show that there is no extreme state in the quantum spectrum of the gravitating shell, as in the case of extreme black hole.