Séminaires sur les aspects théoriques et expérimentaux de la gravitation

Extracting black-hole rotational energy : The generalized Penrose process

by Prof. Jean-Pierre LASOTA (Institut d’Astrophysique de Paris & N. Copernicus Astronomical Center, Warsaw, Poland)

Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)

Amphithéâtre Léon Motchane

Institut des Hautes Etudes Scientifiques

Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette
Relativistic jets are often launched from the vicinity of accreting black holes. They are observed to be produced in stellar-mass black-hole binary systems and are believed to be the fundamental part of the gamma-ray burst phenomenon. Powerful relativistic jets are also ejected by accreting supermassive black holes in some active galactic nuclei. There is no doubt that the jet-launching mechanism is related to accretion onto black holes, but there has been no general agreement as to the ultimate source of energy of these spectacular high energy phenomena. In principle, relativistic jets can be powered either by the black hole gravitational pull or by its rotation (spin), with large-scale magnetic fields invoked as energy extractors in both cases. In the context of strongly magnetized jets Blandford & Znajek (1977) proposed a model of electromagnetic extraction of black hole's rotational energy based on the analogy with the classical unipolar induction phenomenon. The physical meaning of this process has been subject to a long controversy. I will show that the Blanford-Znajek process is a Penrose process of black-hole energy extraction. I will first consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor and show that the necessary and sufficient condition for extraction of a black hole's rotational energy is analogous to that in the mechanical Penrose process: absorption of negative energy and negative angular momentum. I will show that a necessary condition for the Penrose process to occur is for the Noether current to be spacelike or past directed (timelike or null) on some part of the horizon. In the particle ("mechanical") case, the general criterion for the occurrence of a Penrose process reproduces the standard result. For stationary, force-free electro-magnetic field one recovers the condition obtained by Blandford and Znajek in their original article. In the case of relativistic jet-producing ``magnetically arrested disks'' I will show that the negative energy and angular-momentum absorption condition is obeyed when the Blandford-Znajek mechanism is at work, and hence the high energy extraction efficiency up to ~300 % found in recent numerical simulations of such accretion flows results from tapping the black hole's rotational energy through the Penrose process. I will show how black-hole rotational energy extraction works in this case by describing the Penrose process in terms of the Noether current.