The present work proposes a new formalism for the inner regions of a neutrino-dominated accretion flows (NDAFs) by considering the self-gravity, where the neutrino opacity is high enough to make neutrinos trapped becoming a dominant factor in the transportation of energy and angular momentum over the magneto rotational instability. We investigate the possibility of gravitational instability and fragmentation to model the highly variable structure of the prompt emission in gamma-ray bursts (GRBs). The results lead us to introduce the gravitational instability, in these inner regions, as a source of a new viscosity that is of the same functional form as that of the β-prescription of viscosity. Such a consideration brings about fragmentation in the unstable inner disc. In addition, we find the consequent clumpy structure of this area capable to account for the temporal variability of GRB’s light curve, especially for the lower choices of the parameter β, ∼10−5. Finally, we predict the formation of gravitational waves through the migration of fragments before being tidally disrupted. These waves appear to be detectable via a range of current and future detectors from LIGO to Cosmic Explorer.

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