Lasota, J.-P.Gourgoulhon, E.Abramowicz, M.Tchekhovskoy, A.Narayan, Ramesh2016-08-032014Lasota, J.-P., E. Gourgoulhon, M. Abramowicz, A. Tchekhovskoy, and R. Narayan. 2014. “Extracting Black-Hole Rotational Energy: The Generalized Penrose Process.” Phys. Rev. D 89 (2) (January). doi:10.1103/physrevd.89.024041.1550-7998http://nrs.harvard.edu/urn-3:HUL.InstRepos:27802022In the case involving particles the necessary and sufficient condition for the Penrose process to extract energy from a rotating black hole is absorption of particles with negative energies and angular momenta. No torque at the black-hole horizon occurs. In this article we consider the case of arbitrary fields or matter described by an unspecified, general energy-momentum tensor Tµν 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. We also show that a necessary condition for the Penrose process to occur is for the Noether current (the conserved energy-momentum density vector) to be spacelike or past directed (timelike or null) on some part of the horizon. In the particle case, our general criterion for the occurrence of a Penrose process reproduces the standard result. In the case of relativistic jetproducing “magnetically arrested disks” we 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. We show how black-hole rotational energy extraction works in this case by describing the Penrose process in terms of the Noether current.en-USJournal Article2016-08-0310.1103/PhysRevD.89.024041