Scattering Cross Section and Stability of Global Monopoles

TL;DR

This paper investigates how boundary conditions at the origin influence scalar wave scattering and stability in global monopole spacetimes, revealing that different conditions alter the scattering cross section without necessarily causing instability.

Contribution

It demonstrates the impact of boundary conditions on wave scattering and stability analysis in global monopole backgrounds, highlighting their physical significance.

Findings

Boundary conditions affect the differential cross section.

Certain boundary conditions do not induce instability.

Backscattered wave amplitude reveals boundary conditions.

Abstract

We study the scattering of scalar waves propagating on the global monopole background. Since the scalar wave operator in this topological defect is not essentially self-adjoint, its solutions are not uniquely determined until a boundary condition at the origin is specified. As we show, this boundary condition manifests itself in the differential cross section and can be inferred by measuring the amplitude of the backscattered wave. We further demonstrate that whether or not the spacetime is stable under scalar perturbations also relies on the chosen boundary condition. In particular, we identify a class of such boundary conditions which significantly affects the differential cross section without introducing an instability.