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.