On the GeV emission of the type I BdHN GRB 130427A

Abstract: We propose that the "inner engine" of a type I binary-driven hypernova (BdHN) is composed of a Kerr black hole (BH) in a non-stationary state, embedded in a uniform magnetic field $B_0$ aligned with the BH rotation axis, and surrounded by an ionized plasma of extremely low density of $10<sup>{-14}$~g~cm$<sup>{-3}$. Using GRB 130427A as a prototype we show that this "inner engine" acts in a sequence of "elementary impulses". Electrons are accelerated to ultra-relativistic energy near the BH horizon and, propagating along the polar axis, $\theta =0$, they can reach energies of $\sim 10<sup>{18}$ eV, and partially contribute to ultra-high energy cosmic rays (UHECRs). When propagating with ${\theta \neq 0}$ through the magnetic field $B_0$ they give origin by synchrotron emission to GeV and TeV radiation. The mass of BH, $M=2.3 M_\odot$, its spin, $\alpha = 0.47$, and the value of magnetic field $B_0= 3.48 \times 10<sup>{10}$ G, are determined self-consistently in order to fulfill the energetic and the transparency requirement. The repetition time of each elementary impulse of energy ${\cal E} \sim 10<sup>{37}$ erg, is $\sim 10<sup>{-14}$ s at the beginning of the process, then slowly increasing with time evolution. In principle, this "\textit{inner engine}" can operate in a GRB for thousands of years. By scaling the BH mass and the magnetic field the same "inner engine" can describe active galactic nuclei (AGN).