Induced Gravitational Collapse, Binary-Driven Hypernovae, Long Gramma-ray Bursts and Their Connection with Short Gamma-ray Bursts

Short and long Gamma-ray bursts (GRBs) originate in subclasses with specific energy release, spectra, duration, etc, and have binary progenitors. We review here the binary-driven hypernovae (BdHNe) subclass whose progenitor is a CO$_\textrm{core}$-neutron star (NS). The supernova (SN) explosion of the CO$_\textrm{core}$ produces at its center a new NS ($\nu$NS) and triggers a hypercritical accretion onto the NS. The NS can become a more massive NS or collapse into a black hole (BH). We summarize this topic from the first analytic estimates in 2012 to the most recent three-dimensional (3D) smoothed-particle-hydrodynamics (SPH) numerical simulations in 2018. Long GRBs are richer and more complex than previously thought. The SN and the accretion explain X-ray precursors. The NS accretion, its collapse and the BH formation produce asymmetries in the SN ejecta, implying a 3D GRB analysis. The newborn BH surrounded by the ejecta and the magnetic field inherited from the NS, are the \emph{inner engine} from which the electron-positron ($e^+e^-$) plasma and the high-energy emission initiate. The $e^+e^-$ impact on the ejecta converts the SN into a hypernova (HN). The plasma dynamics in the ejecta explains the ultrarelativistic prompt emission in the MeV domain and the mildly-relativistic flares of the early afterglow in the X-ray domain. The feedback of the $\nu$NS emission on the HN explains the X-ray late afterglow and its power-law regime. All the above is in contrast with GRB models attempting to explain all the GRB phases with the kinetic energy of anultrarelativistic jet, as traditionally proposed in the "collapsar-fireball" model. In addition, BdHNe in their different flavors lead to $\nu$NS-NS or $\nu$NS-BH binaries. These binaries merge by gravitational wave emission producing short GRBs, establishing a connection between long and short GRBs and their occurrence rates.