Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes

TL;DR

This paper analyzes the self-force on a static scalar charge in cylindrical thin-shell spacetimes, revealing how the coupling parameter influences the force's behavior and identifying critical values where divergences occur.

Contribution

It provides a detailed study of the self-force in cylindrical thin-shell spacetimes, including analytical and numerical results, and identifies the impact of the curvature coupling on force behavior.

Findings

Critical coupling values cause divergences in the scalar field.

The coupling parameter determines whether the shell acts as a barrier or well.

Asymptotic self-force sign depends on the spacetime's angle deficit or Minkowski nature.

Abstract

We consider the arbitrarily coupled field and self-force of a static massless scalar charge in cylindrical spacetimes with one or two asymptotic regions, with the only matter content concentrated in a thin-shell characterized by the trace of the extrinsic curvature jump $\kappa$. The self-force is studied numerically and analytically in terms of the curvature coupling $\xi$. We found the critical values $\xi_c^{(n)} = n/ ( \rho(r_s)\,\kappa )$, with $n \in \mathbb{N}$ and $\rho(r_s)$ the metric's profile function at the position of the shell, for which the scalar field is divergent in the background configuration. The pathological behavior is removed by restricting the coupling to a domain of stability. The coupling has a significant influence over the self-force at the vicinities of the shell, and we identified $\xi=1/4$ as the value for which the scalar force changes sign at a neighborhood of $r_s$; if $\kappa (1-4\xi)>0$ the shell acts repulsively as an effective potential barrier, while if $\kappa (1-4\xi)<0$ it attracts the charge as a potential well. The sign of the asymptotic self-force only depends on whether there is an angle deficit or not on the external region where the charge is placed; conical asymptotics produce a leading attractive force, while Minkowski regions produce a repulsive asymptotic self-force.