Cosmological gamma-ray bursts are probably powered by systems harboring a rotating black hole. We show that frame-dragging creates baryon-poor outflows in a differentially rotating gap along an open magnetic flux-tube with dissipation P = Ω T (Ω H − 2Ω T )A 2 φ , where 2πA φ denotes the flux in the open tube, for angular velocities Ω H and Ω T of the black hole and the torus, respectively. The output in photon-pair ouflow will be reprocessed in an intervening hypernova progenitor wind or the ISM.
Subject headings: gamma-rays: bursts, theoryCosmological gamma-ray bursts may be powered by rotating black holes following the collapse of young massive stars [33] in hypernovae [21,4] or the coalescence of black holeneutron star binaries [22]. If all black holes are produced by stellar collapse, they should be nearly maximally rotating [1,2], whose mass is relatively high [3,27]. The torus is expected to form from fallback matter stalled against an angular momentum barrier or as the debris of a neutron star following tidal break-up around a Kerr black hole. The torus will provide a similarly-shaped magnetosphere from the remnant magnetic field. The magnetic field strength derives from conservation of magnetic flux and linear amplification (see [21,15]).GRB/afterglow studies indicate an output in ultrarelativistic baryon poor jets. In this Letter, we show that frame-dragging creates powerful photon-pair outflows in a differentially rotating gap along open magnetic flux-tubes supported by black holes in equilibrium with a surrounding torus magnetosphere. This process is continuous and involves no baryonic load. This analysis represents a non-perturbative extension of earlier calculations on pairproduction about the a Wald field [32,26,12].Pair-creation in magnetospheres around rotating black holes is made possible by the Rayleigh criterion, since radiation from the horizon posesses a specific angular momentum at least twice that of the black hole itself. The black hole may support open flux-tubes by an magnetic moment in equilibrium with a surrounding torus magnetosphere. This is a consequence of a no fourth-hair theorem (see below). Frame-dragging introduces Faraday potential drops across these flux-tubes. This creates a competition between local equilibration into a dissipation-free state and current-continuity as a global constraint. Here, currents are determined by slip-slip boundary conditions on the horizon and infinity. As will be shown, the outcome of this competition is dissipation in a differentially rotating gap. This results in the creation of a photon-pair outflow to infinity.A torus surrounding a black hole faces the black hole horizon on the inside and infinity on the outside. These "two faces" are each equivalent in poloidal topology to pulsar magnetospheres with commensurate causal interactions, as shown in Fig. 1. The inner face of the torus receives energy and angular momentum, as does a pulsar when infinity wraps around it (see Fig. 2 of [25]); the outer face always looses energy and angular momentum s...