Rainbow scattering in the gravitational field of a compact object
AbstractWe study the elastic scattering of a planar wave in the curved spacetime of a compact object such as a neutron star, via a heuristic model: a scalar field impinging upon a spherically symmetric uniform density star of radius R and mass M. For R<rc, there is a divergence in the deflection function at the light-ring radius rc=3GM/c2, which leads to spiral scattering (orbiting) and a backward glory; whereas for R>rc, there instead arises a stationary point in the deflection function which creates a caustic and rainbow scattering. As in nuclear rainbow scattering, there is an Airy-type oscillation on a Rutherford-like cross section, followed by a shadow zone. We show that, for R∼3.5GM/c2, the rainbow angle lies close to 180°, and thus there arises enhanced backscattering and glory. We explore possible implications for gravitational wave astronomy and dark matter models.