  In the binary-driven hypernova model of long gamma-ray bursts, a
carbon-oxygen star explodes as a supernova in presence of a neutron star binary
companion in close orbit. Hypercritical (i.e. highly super-Eddington) accretion
of the ejecta matter onto the neutron star sets in, making it reach the
critical mass with consequent formation of a Kerr black hole. We have recently
shown that, during the accretion process onto the neutron star, fast neutrino
flavour oscillations occur. Numerical simulations of the above system show that
a part of the ejecta keeps bound to the newborn Kerr black hole, leading to a
new process of hypercritical accretion. We here address, also for this phase of
the binary-driven hypernova, the occurrence of neutrino flavour oscillations
given the extreme conditions of high density (up to $10^{12}$ g cm$^{-3}$) and
temperatures (up to tens of MeV) inside this disk. We estimate the
\textcolor{red}{behaviour} of the electronic and non-electronic neutrino
content within the two-flavour formalism ($\nu_{e}\nu_{x}$) under the action of
neutrino collective effects by neutrino self-interactions. We find that in the
case of inverted mass hierarchy, neutrino oscillations inside the disk have
frequencies between $\sim (10^{5}$-$10^{9})$ s$^{-1}$, leading the disk to
achieve flavour equipartition. This implies that the energy deposition rate by
neutrino annihilation ($\nu + \bar{\nu} \to e^{-} + e^{+}$) in the vicinity of
the Kerr black hole, is smaller than previous estimates in the literature not
accounting by flavour oscillations inside the disk. The exact value of the
reduction factor depends on the $\nu_{e}$ and $\nu_{x}$ optical depths but it
can be as high as $\sim 5$. The results of this work are a first step toward
the analysis of neutrino oscillations in a novel astrophysical context and, as
such, deserve further attention.
