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.

Quasinormal modes from Penrose limits

“…Given that both the angular momentum and the frequency are approximately real for large real frequency QNMs, these are closely related to Regge poles in this limit. Nevertheless, the complex angular momentum technique in which the Regge poles play an important role, is a useful complementary approach to the problem of black hole scattering more generally [136][137][138][139]. Therefore, to understand the full scattering problem in terms of Penrose limits, it would be interesting to investigate how Regge poles fit in with this approach.…”

Electromagnetic radiation generated by a charged particle falling radially into a Schwarzschild black hole: A complex angular momentum description

“…We would also like to go beyond the case of BHs by considering that of neutron stars and white dwarfs. In this context, the recent CAM analysis of scattering by compact objects [36] could be a natural starting point.…”