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The structure of a hydrodynamic, double transonic flow driven by neutrinoannihilation in the polar region of a Schwarzschild black hole is computed fordifferent energy deposition profiles. The requirement that both, the inflowinto the black hole and the outflow to infinity pass smoothly through theirsonic points fixes the stagnation radius and stagnation pressure. Theasymptotic power of the outflow is shown to be the integral of the energydeposition rate above the stagnation radius. The outflow production efficiencydepends on the energy deposition profile, and is generally higher for shallowerprofiles. Using recent calculations of the neutrino annihilation rate, weestimate that over 50 percents of the total energy deposited above the horizoncan emerge in the form of a relativistic outflow at infinity. The continuouscreation of plasma during the expansion of the outflow leads to generation of alarge specific entropy. This has important implications for the promptphotospheric emission in GRBs.

Ultra-relativistic, neutrino driven flows in GRBs: A double transonic flow solution in Schwarzschild spacetime