On the Short GRB GeV emission from a Kerr Black hole

It has recently become clear that in both short and long gamma-ray bursts (GRBs) it coexists a sequence of different events, each characterized by specific physical processes and corresponding values of the Lorentz gamma factors. The ultra-relativistic prompt emission (UPE) phase, with Lorentz factor $\Gamma\leq10^4$, is followed by a mildly relativistic plateau-afterglow phase with $\Gamma\lesssim2$. The GeV radiation, with $\Gamma\lesssim50$, coexists with the above two phases. It is shown that: a) the GeV radiation originates at the onset of the formation of a black hole (BH), b) its luminosity follows specific power-law dependence when measured in the rest frame of the source with a decay index $\gamma=-1.29\pm0.06$ in the case of the short GRBs, and $\gamma=-1.20\pm0.04$ in the case of the long GRBs, c) these energetics requirements are used to derive the mass and spin of the BH originating this extended GeV emission. We present these conceptual results for the case of short GRBs in this article and give the extended analysis for long GRBs in a companion article. A direct astrophysical application of these results is that the merger of binary neutron stars leading to BH formation emits GeV radiation: the GeV emission is a necessary and sufficient condition to indicate the creation of a BH in S-GRBs.