# Rainbow scattering in the gravitational field of a compact object

## TL;DR

This paper investigates how waves scatter around compact objects like neutron stars, revealing phenomena such as rainbow and glory scattering, with potential implications for gravitational wave detection and dark matter research.

## Contribution

It introduces a heuristic model analyzing scalar wave scattering in curved spacetime, highlighting the conditions for rainbow and glory scattering near compact objects.

## Key findings

- Rainbow scattering occurs for R < r_c, with spiral trajectories and backward glory.
- Rainbow angle approaches 180° near R ≈ 3.5 GM/c^2, enhancing back-scattering.
- Distinct Airy oscillations and shadow zones are observed in the scattering cross section.

## Abstract

We 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 $R < r_c$, there is a divergence in the deflection function at the light-ring radius $r_c = 3GM/c^2$, which leads to spiral scattering (orbiting) and a backward glory; whereas for $R > r_c$ 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 $R \sim 3.5 GM/c^2$, the rainbow angle lies close to $180^\circ$, and thus there arises enhanced back-scattering and glory. We explore possible implications for gravitational wave astronomy, and dark matter models.