Abstract We investigate the relativistic, viscous, advective neutrino-dominated accretion flows (NDAFs) around rotating stellar-mass black holes, incorporating neutrino cooling. By adopting an effective potential to describe the spacetime geometry around the rotating black holes, we self-consistently solve the governing NDAF equations to obtain global transonic accretion solutions. Our findings indicate that, depending on the model parameters, namely, energy (ε), angular momentum (λ), accretion rate ( m ̇ ), viscosity (α), and black hole spin (a k), NDAFs may harbor standing shocks where the Rankine–Hugoniot shock conditions are satisfied. Utilizing these shock-induced NDAF solutions, we compute the neutrino luminosity (L ν ) and neutrino annihilation luminosity ( L ν ν ¯ ) across a wide range of model parameters. We further calculate maximum neutrino luminosity ( L ν max ) and neutrino annihilation luminosity ( L ν ν ¯ max ), resulting in L ν max ∼ 1 0 51 − 53 erg s−1 (1048−51 erg s−1) and L ν ν ¯ max ∼ 1 0 48 − 52 erg s−1 (1042−49 erg s−1) for a k = 0.99 (0.0). These findings suggest that shocked NDAF solutions are potentially promising to explain the energy output of gamma-ray bursts (GRBs). We employ our NDAF model formalism to elucidate L ν ν ¯ obs for five GRBs with known redshifts and estimate their accretion rate ( m ̇ ) based on the spin (a k) of the central source of the GRBs studied here.
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