Scattering from compact objects: Debye series and Regge-Debye poles

Abstract

We investigate elastic scattering by a compact, horizonless body in curved spacetime, considering a massless scalar wave incident on a static, spherically symmetric, uniform-density star of radius $R$ and mass $M$ with a Schwarzschild exterior. We introduce an exact Debye-series decomposition of the scattering matrix, in the spirit of Debye expansions in Mie scattering. This decomposition separates direct surface reflection from contributions involving transmission into the interior and subsequent propagation, and admits a natural trajectory interpretation. We then determine the associated Regge-Debye pole spectrum in the complex angular-momentum plane. For neutron-star-like tenuities ($R>3M$), the spectrum exhibits two pole families: a surface-wave branch associated with the surface matching condition and a broad-resonance branch associated with the interior regularity condition. For ultracompact objects ($R<3M$), the surface-wave branch persists, while the interior-resonance sector splits into broad- and narrow-resonance branches. We next reconstruct the scattering amplitude from the Debye partial-wave contributions and find excellent agreement with direct partial-wave calculations. Finally, we develop complex angular-momentum representations order by order in the Debye series, making explicit how the pole families and non-pole sectors contribute to each Debye term. In the neutron-star-like regime, we find a genuine competition between Regge-Debye pole sums and branch-cut contributions, and show that, at high frequency, the rainbow-like enhancement already arises from the first interior-transmission contribution and is dominated by the interior-resonance Regge-Debye poles. By contrast, in the ultracompact regime, the Debye amplitudes are overwhelmingly pole dominated.

23 pages, 11 figures, v2: Minor changes and a few typos corrected in the text to match the published version

References in corpus (26)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Testing the nature of dark compact objects: a status report
• First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metric
• Universality of high-energy absorption cross sections for black holes
• Scattering and absorption of gravitational plane waves by rotating black holes
• Gravitational wave echoes from black hole area quantization
• Scattering of scalar waves by rotating black holes
• Fine structure of high-energy absorption cross sections for black holes
• Electromagnetic wave scattering by Schwarzschild black holes
• Complex angular momentum in black hole physics and quasinormal modes
• Regge poles of the Schwarzschild black hole: a WKB approach
• Wave Optics in Spacetimes with Compact Gravitating Object
• Regge pole description of scattering of scalar and electromagnetic waves by a Schwarzschild black hole
• Black hole interference patterns in flavour oscillations
• Regge pole description of scattering of gravitational waves by a Schwarzschild black hole
• Rainbow scattering in the gravitational field of a compact object
• Scattering from compact objects: Regge poles and the complex angular momentum method
• An alternative description of gravitational radiation from black holes based on the Regge poles of the $\mathcal{S}$-matrix and the associated residues
• Rainbow scattering of gravitational plane waves by a compact body
• Regge pole description of scattering by dirty black holes
• Eclipses of continuous gravitational waves as a probe of stellar structure
• Black hole absorption cross sections: Spin and Regge poles
• Self-force and the Schwarzschild star