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In a new classification of merging binary neutron stars (NSs) we separateshort gamma-ray bursts (GRBs) in two sub-classes. The ones with$E_{iso}\lesssim10^{52}$ erg coalesce to form a massive NS and are indicated asshort gamma-ray flashes (S-GRFs). The hardest, with $E_{iso}\gtrsim10^{52}$erg, coalesce to form a black hole (BH) and are indicated as genuine short-GRBs(S-GRBs). Within the fireshell model, S-GRBs exhibit three differentcomponents: the P-GRB emission, observed at the transparency of aself-accelerating baryon-$e^+e^-$ plasma; the prompt emission, originating fromthe interaction of the accelerated baryons with the circumburst medium; thehigh-energy (GeV) emission, observed after the P-GRB and indicating theformation of a BH. GRB 090510 gives the first evidence for the formation of aKerr BH or, possibly, a Kerr-Newman BH. Its P-GRB spectrum can be fitted by aconvolution of thermal spectra whose origin can be traced back to an axiallysymmetric dyadotorus. A large value of the angular momentum of the newborn BHis consistent with the large energetics of this S-GRB, which reach in the1--10000 keV range $E_{iso}=(3.95\pm0.21)\times10^{52}$ erg and in the 0.1--100GeV range $E_{LAT}=(5.78\pm0.60)\times10^{52}$ erg, the most energetic GeVemission ever observed in S-GRBs. The theoretical redshift $z_{th}=0.75\pm0.17$that we derive from the fireshell theory is consistent with the spectroscopicmeasurement $z=0.903\pm0.003$, showing the self-consistency of the theoreticalapproach. All S-GRBs exhibit GeV emission, when inside the Fermi-LAT field ofview, unlike S-GRFs, which never evidence it. The GeV emission appears to bethe discriminant for the formation of a BH in GRBs, confirmed by their observedoverall energetics.

GRB 090510: a genuine short-GRB from a binary neutron star coalescing into a Kerr-Newman black hole