Magnetic collimation of relativistic jets: the role of the black hole spin

An ideal engine for producing ultrarelativistic jets is a rapidly rotating black hole threaded by a magnetic field. Following the 3+1 decomposion of spacetime of Thorne et al . (1986), we use a local inertial frame of reference attached to an observer comoving with the frame-dragging of the Kerr black hole (ZAMO) to write the GRMHD equations. Assuming θ-self similarity, analytical solutions for jets can be found for which the streamline shape is calculated exactly. Calculating the total energy variation between a non polar streamline and the polar axis, we have extended to the Kerr metric the simple criterion for the magnetic collimation of jets developed by Sauty et al . (1999). We show that the black hole rotation induces a more efficient magnetic collimation of the jet.