*2.3. Models of Jet-Launching Central Engines*

The leading jet-launching mechanism, by analogy with other relativistic jets such as those observed in active galactic nuclei (AGN, [96]) and microquasars [97,98], is the Blandford–Znajek (BZ) mechanism [70]. This is a process by which the rotational energy of a spinning black hole (BH) is extracted in presence of a large-scale, poloidal magnetic field threading the horizon. The magnetic field is sustained by an accretion disk, and the mechanism requires the formation of a "force-free" [99] magnetosphere close to the poles of the BH, which is only possible when the magnetic field energy density in the polar region exceeds the rest-mass energy density. In other words, a low-density funnel must be present along the BH rotation axis, and this is the region where the jet forms. The jet luminosity produced by the process follows [70]

*L*BZ ∝ *B* <sup>2</sup>*M*<sup>2</sup> BH*a* 2 , (3)

with higher-order (*a* 4 ) corrections when *a* approaches unity [100,101]. Here, *B* is the strength of the radial component of the magnetic field at the horizon, *M*BH is the black hole's gravitational mass and *a* is its dimensionless spin parameter. The normalization constant depends on the magnetic field geometry and on the accretion disk properties [100]. Typical expected values in the GRB context are *<sup>L</sup>*BZ <sup>∼</sup> <sup>10</sup><sup>49</sup> <sup>−</sup> <sup>10</sup><sup>51</sup> erg/s, which match the loose observational luminosity constraints set by the observed gamma-ray energies and durations, and by the collimation angles inferred from afterglow observations (see Section 3.1). Jets launched by this process are expected to start off as magnetically-dominated outflows (i.e., *σ* 1 at the jet base).

Alternative jet-launching scenarios include energy deposition by neutrino-antineutrino (*νν*¯) pair annihilation in the funnel above the BH [102–107], and a proto-magnetar central engine [71,108–110]. The *νν*¯ luminosity for the former mechanism could be provided by the hot, inner parts of the accretion disk [111], and a jet-powered by such a process would be dominated by internal energy (*η*/*ρ* 0 *c* <sup>2</sup> 1) at its base, which would then be converted to kinetic energy by hydrodynamic acceleration. We note, though, that the *νν*¯ mechanism seems unable to explain the large luminosities [112] and energies [107] of some GRBs, and global simulations of jet launching in the aftermath of a binary neutron star merger seem to indicate that a jet powered by such mechanism would be unable to break out of the dense ejecta cloud that surrounds the merger remnant [113].
