We investigate the physical properties of the central engine powering gamma-ray bursts (GRBs), modeled as a stellar-mass black hole accreting via a neutrino-dominated accretion flow (NDAF). By solving the governing hydrodynamic equations, we obtain global transonic NDAF solutions featuring shock transitions and examine their role in powering GRB energetics. The NDAF solutions are explored over a broad range of black hole parameters, including its mass ($M_{\mathrm{BH}}$) and spin ($a_{\mathrm{k}}$), and accretion rate ($\dot{M}$). We find that shocked NDAFs can naturally account for the observed diversity in GRB energy output. Incorporating results from numerical simulations of binary neutron star and black hole-neutron star mergers, we estimate the remnant black hole mass and spin parameters for the predicted range of postmerger disk mass ($M_{\mathrm{disk}}$). Our analysis reveals that small-mass black holes with relatively low spin values can adequately reproduce the luminosities of short GRBs (SGRBs), whereas identical GRB luminosities can also be achieved for more massive black holes possessing higher spin values. Finally, we uncover a robust correlation between the black hole spin and disk mass such that $M_{\mathrm{disk}}$ decreases with increasing $a_{\mathrm{k}}$, remaining largely independent of the black hole mass ($M_{\mathrm{BH}}$) powering GRBs.

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• Gamma ray bursts
• Accretion disk & black-hole plasma
• Classical black holes