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

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.

v2: minor changes and a few typos corrected in the text to match the published version. We have also added two paragraphs (Sec.IIID) to discuss the limit $\alpha \to 0$, and different stellar models with continuous potentials at the surface

References in corpus (26)

• Light rings as observational evidence for event horizons: long-lived modes, ergoregions and nonlinear instabilities of ultracompact objects
• Black hole ringdown: the importance of overtones
• Universality of high-energy absorption cross sections for black holes
• Scattering and absorption of gravitational plane waves by rotating black holes
• Fermion scattering by a Schwarzschild black hole
• 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
• Scattering from charged black holes and supergravity
• Scattering of Long-Wavelength Gravitational Waves
• Partial wave analysis of the Dirac fermions scattered from Schwarzschild black holes
• 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
• Spectral lines of extreme compact objects
• 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
• On-axis scattering of scalar fields by charged rotating black holes
• On the Inverse Spectrum Problem of Neutron Stars
• Eclipses of continuous gravitational waves as a probe of stellar structure
• High-frequency behavior of w-mode pulsations of compact stars
• Gravitons scattering from classical matter
• Scattering of massless scalar waves by magnetically charged black holes in Einstein-Yang-Mills-Higgs theory

Cited by in corpus (14)

• Pseudospectrum and black hole quasi-normal mode (in)stability
• Ringdown stability: greybody factors as stable gravitational-wave observables
• Tidal response from scattering and the role of analytic continuation
• From black hole spectral instability to stable observables
• Regge pole description of scattering by dirty black holes
• Scattering of massless scalar field by charged dilatonic black holes
• Gravitational waves in massive gravity: Waveforms generated by a particle plunging into a black hole and the excitation of quasinormal modes and quasibound states
• Electromagnetic radiation generated by a charged particle falling radially into a Schwarzschild black hole: A complex angular momentum description
• Scattering and conversion of electromagnetic and gravitational waves by Reissner-Nordström black holes: The Regge pole description
• Probing the conformal invariance around the nonsingular static spherical black holes with waves
• Spontaneous particle creation by oscillating compact stars
• Quasinormal mode frequencies of Kerr black holes from Regge trajectories
• Scattering from compact objects: Debye series and Regge-Debye poles
• Dynamical system approach to the spectral (in)stability of black holes under localised potential perturbations