  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. 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. We give a detailed study of these geodesics and give
several numerical examples. Among them are a set of perfectly collimated
geodesics with asymptotes $\rho =\rho_{1}$ parallel to the $z-$ axis, with
$\rho_{1}$ only depending on the ratios $\frac{\mathcal{Q}}{E^{2}-1}$ and
$\frac{a}{M}$, where $a$ and $M$ are the parameters of the Kerr black hole, $E$
the particle energy and $\mathcal{Q}$ the Carter's constant.

General Relativity and Quantum Cosmology;Astrophysics