Quantum Singularities in Spacetimes with Spherical and Cylindrical Topological Defects

TL;DR

This paper investigates quantum behavior near spacetime singularities caused by spherical and cylindrical topological defects, analyzing the need for boundary conditions in solutions of the Klein-Gordon equation.

Contribution

It provides exact solutions to Einstein equations with delta-function curvature on shells and examines the implications for quantum particles and boundary conditions.

Findings

Quantum particles require specific boundary conditions at shells.

Exact solutions exist for spacetimes with delta-function curvature.

The study clarifies the role of boundary conditions in quantum singularities.

Abstract

Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the curvature is represented by a Dirac delta function with support either on a sphere or on a cylinder (spherical and cylindrical shells). In particular, we analyze the necessity of extra boundary conditions on the shells.