Kerr geodesics, the Penrose process and jet collimation by a black hole

¹ LERMA-UPMC, Université Pierre et Marie Curie, Observatoire de Paris, CNRS, UMR 8112, 3 rue Galilée, 94200 Ivry-sur-Seine, France e-mail: jerome.gariel@upmc.fr; gmarcilhacy@hotmail.com
² School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, UK e-mail: m.a.h.maccallum@qmul.ac.uk
³ Laboratório Nacional de Computação Científica, 25651-070 Petrópolis RJ, Brazil e-mail: nilton.santos@upmc.fr

Received: 16 November 2009
Accepted: 10 February 2010

Abstract

Aims. We re-examine the possibility that astrophysical jet collimation may arise from the geometry of rotating black holes and the presence of high-energy particles resulting from a Penrose process, without the help of magnetic fields.

Methods. Our analysis uses the Weyl coordinates, which are revealed better adapted to the desired shape of the jets. We numerically integrate the 2D-geodesics equations.

Results. We give a detailed study of these geodesics and give several numerical examples. Among them are a set of perfectly collimated geodesics with asymptotes ρ = parallel to the z-axis, with only depending on the ratios and , where a and M are the parameters of the Kerr black hole, E the particle energy and the Carter's constant.