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We calculate the Regge poles of the scattering matrix for a gravitatingcompact body, for scalar fields and for gravitational waves in the axialsector. For a neutron-starlike body, the spectrum exhibits two distinctbranches of poles, labeled surface waves and broad resonances; for ultracompactobjects, the spectrum also includes a finite number of narrow resonances. Weshow, via a WKB analysis, that the discontinuity of the effective potential atthe body's surface determines the imaginary component of the broad-resonancepoles. Next, we examine the role of Regge poles in the time-independentscattering of monochromatic planar waves. We apply complex angular momentumtechniques 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 sectionat several frequencies, and show precise agreement with the partial-wavecalculations. Finally, we show that compact bodies naturally give rise toorbiting, glory, and rainbow-scattering interference effects.

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