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We first refine the fixed concept in the literature that the usage of theNewtonian potential in studies of black hole accretion is invalid and thegeneral relativistic effect must be considered. As our main results, we thenshow that the energy released by neutrino annihilation in neutrino-dominatedaccretion flows is sufficient for gamma-ray bursts when the contribution fromthe optically thick region of the flow is included, and that in the opticallythick region advection does not necessarily dominate over neutrino coolingbecause the advection factor is relevant to the geometrical depth rather thanthe optical depth of the flow.Comment: 11 pages, 3 figures, accepted by ApJ Letter

Neutrino-dominated Accretion Models for Gamma-Ray Bursts: Effects of General Relativity and Neutrino Opacity