On Born approximation in black hole scattering

TL;DR

This paper derives explicit formulas for massless scalar scattering off black holes using the Born approximation, discusses its limitations in extracting quasinormal modes, and proposes a new method for analyzing large imaginary parts of these modes.

Contribution

It introduces a novel method to extract large imaginary parts of quasinormal modes using Coulomb-like phase shifts, addressing limitations of the traditional Born approximation.

Findings

Born approximation conditions prevent straightforward quasinormal mode extraction.

The Born approximation is not very accurate for scattering of various waves from black holes.

A new method using Coulomb-like phase shifts is proposed for analyzing quasinormal modes.

Abstract

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner-Nordstr\"{o}m and Reissner-Nordstr\"{o}m-de Sitter backgrounds is considered. In particular, explicit formulae in terms of transcendental functions for the scattering of massless scalar particles off black holes are derived within a Born approximation. It is shown that the conditions on the existence of the Born integral forbid a straightforward extraction of the quasi normal modes using the Born approximation for the scattering amplitude. Such a method has been used in literature. We suggest a novel, well defined method, to extract the large imaginary part of quasinormal modes via the Coulomb-like phase shift. Furthermore, we compare the numerically evaluated exact scattering amplitude with the Born one to find that the approximation is not very useful for the scattering of massless scalar, electromagnetic as well as gravitational waves from black holes.