Scattering from compact objects: Regge poles and the complex angular momentum method

TL;DR

This paper investigates the Regge poles of the scattering matrix for compact gravitating bodies, revealing their spectral properties, and applies complex angular momentum methods to analyze scattering phenomena like orbiting and rainbow effects.

Contribution

It introduces a detailed analysis of Regge poles for compact objects, linking surface properties to resonance spectra and applying complex angular momentum techniques to scattering calculations.

Findings

Regge pole spectra differ for neutron-star-like and ultracompact bodies.

Discontinuities in the effective potential influence resonance widths.

Complex angular momentum methods accurately reproduce scattering cross sections.

Abstract

We calculate the Regge poles of the scattering matrix for a gravitating compact body, for scalar fields and for gravitational waves in the axial sector. For a neutron-starlike body, the spectrum exhibits two distinct branches of poles, labeled surface waves and broad resonances; for ultracompact objects, the spectrum also includes a finite number of narrow resonances. We show, via a WKB analysis, that the discontinuity of the effective potential at the body's surface determines the imaginary component of the broad-resonance poles. Next, we examine the role of Regge poles in the time-independent scattering of monochromatic planar waves. We apply complex angular momentum techniques to re-sum the partial wave series for the scattering amplitude, expressing it as a residue series evaluated at poles in the first quadrant, accompanied by a background integral. We compute the scattering cross section at several frequencies, and show precise agreement with the partial-wave calculations. Finally, we show that compact bodies naturally give rise to orbiting, glory, and rainbow-scattering interference effects.