Scalar self-force effects in neutral $W$-soliton backgrounds

TL;DR

This paper studies the properties of the $W$-soliton solution, analyzing particle scattering, scalar field propagation, and energy loss, with a focus on scalar self-force effects in these backgrounds.

Contribution

It provides a detailed analysis of scalar self-force effects in $W$-soliton backgrounds, including scattering angles, quasi-normal modes, and energy loss, with fully analytic results.

Findings

Derived exact and approximate scattering angles.

Computed quasi-normal mode spectra analytically.

Presented energy loss in a Post-Newtonian expansion.

Abstract

We investigate several geometrical and physical properties of the recently found $W$-soliton solution (neutral case). We discuss both the genuine 5d solution and its reduction to 4d and highlight similarities and differences. In both cases, we study scattering processes of massless and massive particles in the background, reconstructing the gauge-invariant scattering angle, either with exact expressions or with large-angular momentum expansion expressions, which we show how to resum in a useful form. Finally, we analyze the propagation of a test scalar field in the $W$-soliton background and compute the spectrum of Quasi Normal Modes in the case of (non-)minimal coupling and the radiated energy in the case of minimal coupling. Our result for the energy loss is fully analytic and presented in a Post-Newtonian expansion, following the approach termed gravitational self force.