Scalar self-force effects in neutral $W$-soliton backgrounds
Massimo Bianchi, Donato Bini, Giorgio Di Russo
TL;DR
The paper addresses the scalar self-force and wave dynamics in the neutral W-soliton backgrounds, both in five dimensions and after reduction to four dimensions, to understand microstate-like geometries without horizons. It combines exact and large-angular-momentum scattering analyses with Newman-Penrose structure and perturbations, and develops a gravitational self-force-inspired framework for scalar energy loss. Key contributions include a full PN expansion of scalar energy loss along circular orbits, a robust MST/JWKB/Leaver treatment of QNMs in the 4d case, and a detailed comparison against Schwarzschild and Top-Star backgrounds to illuminate strong-field differences. The findings offer analytic control over wave propagation in horizonless solitonic spacetimes and set the stage for extensions to charged solitons and genuine gravitational waves, with potential implications for black-hole microstate geometries and holographic correspondences.
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.