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The present work proposes a new formalism for the inner regions of aneutrino-dominated accretion flows (NDAFs) by considering the self-gravity,where the neutrino opacity is high enough to make neutrinos trapped becoming adominant factor in the transportation of energy and angular momentum over themagneto rotational instability. We investigate the possibility of gravitationalinstability and fragmentation to model the highly variable structure of theprompt emission in gamma-ray bursts (GRBs). The results lead us to introducethe gravitational instability, in these inner regions, as a source of a newviscosity which is of the same functional form as that of the$\beta$-prescription of viscosity. Such a consideration brings aboutfragmentation in the unstable inner disk. In addition, we find the consequentclumpy structure of this area capable to account for the temporal variabilityof GRB's light curve, especially for the lower choices of the parameter$\beta$, $\sim 10^{-5}$. Finally, we predict the formation of gravitationalwaves through the migration of fragments before being tidally disrupted. Thesewaves appear to be detectable via a range of current and future detectors fromLIGO to Cosmic Explorer.

GRB variabilities and following gravitational waves induced by gravitational instability in NDAFs