Eur. Phys. J. C (2011) 71: 1831
https://doi.org/10.1140/epjc/s10052-011-1831-y

Regular Article - Theoretical Physics

On Born approximation in black hole scattering

¹ Department of Mathematics, University of West Indies, Kingston 6, Jamaica
² Departamento de Fisica, Universidad de los Andes, Cra.1E No.18A-10, Bogota, Colombia

^* e-mail: mnowakos@uniandes.edu.co

Received: 4 October 2011
Revised: 2 November 2011
Published online: 7 December 2011

Abstract

A massless field propagating on spherically symmetric black hole metrics such as the Schwarzschild, Reissner–Nordström and Reissner–Nordström–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.